Polar Coding Method and Apparatus

ABSTRACT

Example polar coding methods and apparatus are described. One example method includes determining a sequence used to code to-be-coded bits. Polar coding is performed on the to-be-coded bits by using the sequence to obtain coded bits. The sequence is used to represent a reliability order of N polarized channels, N is a mother code length of a polar code, and N is a positive integer power of 2.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/664,660, filed on Oct. 25, 2019, which is a continuation of U.S.patent application Ser. No. 16/236,002, filed on Dec. 28, 2018, now U.S.Pat. No. 10,511,329, which is a continuation of InternationalApplication No. PCT/CN2018/092908, filed on Jun. 26, 2018, which claimspriority to Chinese Patent Application No. 201710632016.8, filed on Jul.28, 2017. All of the afore-mentioned patent applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

Embodiments of this application relate to the field of communicationstechnologies, and in particular, to a polar coding method and apparatus.

BACKGROUND

As a most basic wireless access technology, channel coding plays acrucial role in ensuring reliable data transmission. In an existingwireless communications system, channel coding is usually performed byusing a turbo code, a low-density parity-check (LDPC) code, and a polarcode. The turbo code cannot support information transmission at anexcessively low or excessively high bit rate. However, for medium-packetor short-packet transmission, it is difficult for the turbo code and theLDPC code to implement desired performance when lengths of the codes arelimited, due to coding/decoding characteristics of the turbo code andthe LDPC code. In terms of implementation, the turbo code and the LDPCcode have relatively high calculation complexity in a coding/decodingimplementation process. Theoretically, it is proved that the polar codeis a good code that can achieve a Shannon capacity and has relativelysimple coding/decoding complexity, and for this reason, the polar codebecomes more widely applied.

However, with rapid evolution of the wireless communications system, afuture communications system, such as a fifth generation (5G)communications system, has some new characteristics. For example, threemost typical communications scenarios include an enhanced mobilebroadband (eMBB) Internet, massive machine type communication (mMTC),and ultra-reliable and low latency communications (URLLC). Thesecommunications scenarios impose a higher requirement on coding/decodingperformance of the polar code.

A reliability order of polarized channels plays an important role in thecoding/decoding performance of the polar code. However, in a currentphase, accuracy of the reliability order of the polarized channels isnot desired. Consequently, further improvement of the coding/decodingperformance of the polar code in an application process is affected.

SUMMARY

Embodiments of this application provide a polar coding method andapparatus, to improve accuracy of a reliability order of polarizedchannels.

According to a first aspect, a polar coding method is provided. At leasttwo sequences with relatively good performance are selected based on aperformance determining rule. Same sequence numbers at a same sortinglocation in the at least two sequences are determined. The determinedsame sequence numbers are determined as sequence numbers whosereliability remains unchanged in sequences, and the sequence numberswhose reliability remains unchanged in the sequences are sorted based onorders of the sequence numbers in the at least two sequences. Sequencenumbers in the at least two sequences other than the determined sequencenumbers whose reliability remains unchanged are compared to select somesubsequences, and locations of elements in the subsequences may bemutually exchanged. A sorting sequence obtained from above is used as asorting sequence used for polar coding in this embodiment of thisapplication. In this way, for the sorting sequence obtained by using theforegoing method, a plurality of sequences with relatively goodperformance can be comprehensively considered, and a sequence numberwhose reliability remains unchanged is determined by using anintersection set between different sequences. This helps improveaccuracy of a reliability order of polarized channels and improvecoding/decoding performance of a polar code.

In a possible design, a sequence used to code to-be-coded bits isdetermined, where the sequence is used to represent a reliability orderof N polarized channels; and polar coding is performed on theto-be-coded bits by using the sequence to obtain coded bits, where N isa mother code length of a polar code, and N is a positive integer powerof 2.

In a possible design, a length of the to-be-coded bits is K, the Kto-be-coded bits are mapped to K polarized channels in the N polarizedchannels, and reliability of the K polarized channels is higher thanreliability of remaining N−K polarized channels.

In a possible design, the sequence used to code the to-be-coded bits isdetermined based on the mother code length N and a preset sequence.

In a possible design, the sequence used to code the to-be-coded bits isall or a subset of another sequence, the another sequence includesN_(max) sequence numbers, the N_(max) sequence numbers are arranged inthe another sequence based on reliability of the N_(max) polarizedchannels, N_(max) is a positive integer power of 2, and N_(max)>N.

In a possible design, the sequence meets a nesting characteristic, andthe nesting characteristic is as follows: A sequence with a relativelyshort mother code length of N₂ is obtained based on a sequence with arelatively long mother code length of N₁. Elements whose sequencenumbers are less than or equal to N₂ are extracted from the sequencewith the relatively long mother code length of N₁, and an obtainedsubsequence is the sequence with the relatively short mother code lengthof N₂. An order of the elements in the obtained sequence with therelatively short mother code length of N₂ is the same as an order ofthese elements in the sequence with the relatively long mother codelength of N₁.

In a possible design, N_(max) is a maximum mother code length of a polarcode, for example, N_(max)=1024, or N_(max)=512. The sequence needs tomeet the nesting characteristic. When a sequence with a maximum mothercode length is determined, another sequence with a relatively shortmother code length may be obtained based on the sequence with themaximum mother code length. For example, a sequence with a length of1024 and whose maximum mother code length is 1024 is determined.Elements whose element values are less than or equal to 64 are extractedfrom the sequence with the length of 1024 to form a subsequence with alength of 64. An order of the elements in the obtained subsequence withthe length of 64 is the same as an order of these elements in thesequence with the length of 1024. That is, the extracted subsequencemeets the nesting characteristic. Similarly, sequences of lengths 128,256, and 512 may be extracted from the sequence with the length of 1024.The obtained sequences with the short mother code lengths are applied inthis embodiment of this application to code the to-be-coded bits.

In a possible design, the sequence may be a part or all of any one ofsequences (1) to (30) in the specification. When N=1024, the sequencemay be a part or all of any one of sequences S1 to S20 in thespecification.

In a possible design, when a value of N is 64, 128, 256, or 512, thesequence may be extracted from a preset sequence with a maximum mothercode length based on the nesting characteristic, or a sequencecorresponding to a code length in the sequences (1) to (30) in thespecification may be directly used.

Polar construction is performed by using the sequence, so as to helpimprove accuracy of evaluating reliability of a polarized channel,thereby improving coding/decoding performance of a polar code.

A minimum value of a sequence number in any one of the sequences S1 toS20 in the specification is 1, and sequence numbers are arranged inascending order of reliability of the N polarized channels. In apossible design, if the sequence numbers in the sequence are arranged inascending order of the reliability of the N polarized channels and aminimum value of the sequence numbers of the sequence is 0, a newsequence is obtained by sequentially subtracting 1 from the sequencenumbers in any sequence, and sequence performance is not affected.

Similarly, in a possible design, if the sequence numbers in the sequenceare arranged in descending order of the reliability of the N polarizedchannels, a new sequence may be obtained by arranging sequence numbersin any one of sequences S1 to S20 in the specification in a reverseorder, and the sequence performance is also not affected.

In a possible design, the sequence may also be represented by using asequence of normalized reliability or equivalent reliability ofchannels. For example, if a sorting location of a channel x in thesequence is n (a minimum sequence number in the sequence is denoted as1), reliability of the channel may be represented by n or normalizedn/N.

In a possible design, locations of a few elements in any one of thesequences S1 to S20 in the specification may be mutually exchanged. Forexample, a location of a sequence number may be adjusted within aspecified amplitude. For example, the specified amplitude is 5, and alocation of an element whose sequence number is 10 may be adjustedwithin a range from five locations on the left of the element to fivelocations on the right of the element.

According to a second aspect, a polar coding apparatus is provided, andthe apparatus has functions of implementing the method according to anyone of the first aspect or the possible designs of the first aspect. Thefunctions may be implemented by using hardware, or may be implemented byhardware executing corresponding software. The hardware or the softwareincludes one or more modules corresponding to the functions.

In a possible design, when some or all of the functions are implementedby using hardware, the polar coding apparatus includes: an inputinterface circuit, configured to obtain to-be-coded bits; a logiccircuit, configured to perform behaviors described in any one of thefirst aspect or the possible designs of the first aspect; and an outputinterface circuit, configured to output a coded bit sequence.

Optionally, the polar coding apparatus may be a chip or an integratedcircuit.

In a possible design, when some or all of the functions are implementedby using software, the polar coding apparatus includes: a memory,configured to store a program; and a processor, configured to executethe program stored in the memory. When the program is executed, thepolar coding apparatus may implement the method according to any one ofthe first aspect or the possible designs of the first aspect.

Optionally, the memory may be a physically independent unit, or may beintegrated into the processor.

In a possible design, when some or all of the functions are implementedby using software, the polar coding apparatus includes a processor. Amemory configured to store a program is located outside the codingapparatus. The processor is connected to the memory by using acircuit/wire, and is configured to read and execute the program storedin the memory.

According to a third aspect, a communications system is provided, wherethe communications system includes a transmit end and a receive end, andthe transmit end may perform the method according to the first aspect orany possible design of the first aspect.

According to a fourth aspect, a computer storage medium is provided,where the computer storage medium stores a computer program, and thecomputer program includes an instruction used to perform the methodaccording to any one of the first aspect or the possible designs of thefirst aspect.

According to a fifth aspect, an embodiment of this application providesa computer program product including an instruction. When theinstruction runs on a computer, the computer performs the method in theforegoing aspect.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic architectural diagram of a communications systemapplied to an embodiment of this application;

FIG. 2 is a schematic flowchart of a polar coding method according to anembodiment of this application;

FIG. 3 is a first schematic structural diagram of a polar codingapparatus according to an embodiment of this application;

FIG. 4 is a second schematic structural diagram of a polar codingapparatus according to an embodiment of this application;

FIG. 5 is a third schematic structural diagram of a polar codingapparatus according to an embodiment of this application; and

FIG. 6 is a fourth schematic structural diagram of a polar codingapparatus according to an embodiment of this application.

DESCRIPTION OF EMBODIMENTS

The following describes in detail the embodiments of this applicationwith reference to the accompanying drawings.

The embodiments of this application provide a polar coding method andapparatus. At least two sequences with relatively good performance areselected based on a performance determining rule. Same sequence numbersat a same sorting location in the at least two sequences are determined.The determined same sequence numbers are determined as sequence numberswhose reliability remains unchanged in sequences, and the sequencenumbers whose reliability remains unchanged in the sequences are sortedbased on orders of the sequence numbers in the at least two sequences.Sequence numbers in the at least two sequences other than the determinedsequence numbers whose reliability remains unchanged are compared toselect some subsequences, and locations of elements in the subsequencesmay be mutually exchanged. A sorting sequence obtained from above isused as a sorting sequence used for polar coding in the embodiments ofthis application. In this way, for the sorting sequence obtained byusing the foregoing method, a plurality of sequences with relativelygood performance can be comprehensively considered, and a sequencenumber whose reliability remains unchanged is determined by using anintersection set between different sequences. This helps improveaccuracy of a reliability order of polarized channels and improvecoding/decoding performance of a polar code.

To facilitate understanding of the embodiments of this application, apolar code is briefly described below.

A coding policy of the polar code is to transmit useful information of auser by using a noiseless channel, and transmit agreed information or noinformation at all on a noisy channel. The polar code is also a linearblock code, a coding matrix of the polar code is G_(N), a coding processis x₁ ^(N)=u₁ ^(N)G_(N), where u₁ ^(N)=(u₁, u₂, . . . , u_(N)) is abinary row vector, a length of u₁ ^(N) (namely, a code length) is N,G_(N) is an N×N matrix, and G_(N)=F₂ ^(⊗(log) ² ^((N))). F₂ ^(⊗(log) ²^((N))) is defined as a kronecker product of log₂ ^(N) matrices F₂. Thematrix

$F_{2} = {\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}.}$

In the coding process of the polar code, some bits in u₁ ^(N) are usedto carry information, and are referred to as an information bit set, anda set of indexes of the information bits is denoted as A. The other bitsare set to fixed values on which a receive end and a transmit endpre-agreed, and are referred to as a fixed bit set or a frozen bit set(frozen bits), and a set of indexes of these bits is represented by acomplementary set A^(c) of A. The coding process of the polar code isequivalent to x₁ ^(N)=u_(A)G_(N)(A)⊗u_(A) _(c) G_(N). (A^(c)) whereG_(N)(A) is a sub-matrix obtained by using rows corresponding to theindexes in the set A, and G_(N) (AC) is a sub-matrix obtained by usingrows corresponding to the indexes in the set A^(c). u_(A) is a set ofinformation bits in u₁ ^(N), and a quantity of the information bits isK. u_(A) _(c) is a set of fixed bits in u₁ ^(N), a quantity of the fixedbits is (N−K), and the fixed bits are known bits. These fixed bits aregenerally set to 0. However, the fixed bits may be set to any valueprovided that the receive end and the transmit end pre-agree on thevalue. Therefore, coding output of the polar code may be simplified asx₁ ^(N)=u_(A)G_(N)(A), where u_(A) is the set of information bits in u₁^(N), u_(A) is a row vector with a length of K, namely, |A|=K, |⋅|indicates a quantity of elements in the set, K is a size of aninformation block, G_(N)(A) is the sub-matrix that is in the matrixG_(N) and that is obtained by using the rows corresponding to theindexes in the set A, and G_(N)(A) is a K×N matrix.

A construction process of the polar code is a selection process of theset A, and determines performance of the polar code. The constructionprocess of the polar code generally includes: determining, based on amother code length N, that there are N polarized channels, where the Npolarized channels respectively correspond to N rows in the codingmatrix; and calculating reliability of the polarized channels, usingindexes of the first K polarized channels with relatively highreliability as elements in the set A, and using indexes corresponding toremaining (N−K) polarized channels as elements in the set A^(c) of theindexes of the fixed bits. The set A determines locations of theinformation bits, and the set A^(c) determines locations of the fixedbits.

A sequence in the embodiments of this application is used to represent areliability order of the N polarized channels. N is a mother code lengthof the polar code, and N is a positive integer power of 2.

In a case, the sequence may include sequence numbers of the N polarizedchannels, and the sequence numbers of the N polarized channels arearranged in the sequence based on reliability of the N polarizedchannels, for example, may be arranged in descending order of thereliability, or may be arranged in ascending order of the reliability.For ease of description, such a sequence is referred to as a Q sequence.

In another case, the sequence may include values of the reliability ofthe N polarized channels. Optionally, the value of the reliability maybe a value of normalized reliability or a value of equivalentreliability. For example, if a sorting location of a channel x in thesequence is y and a minimum sequence number in the sequence is denotedas 1, reliability of the channel may be represented by y or normalizedy/N. Similarly, the values of the reliability of the N polarizedchannels may be arranged in the sequence in descending order of thereliability, or may be arranged in ascending order of the reliability.For ease of description, such a sequence is referred to as a Z sequence.

It can be learned that the Q sequence and the Z sequence may be mutuallyconverted. In other words, the Z sequence may be obtained if the Qsequence is known, and vice versa.

A value of an element in the sequence may range from 0 to N−1, or mayrange from 1 to N. In the embodiments of this application, an example inwhich the value of the element in the sequence ranges from 1 to N isused for description. It can be learned that another sequence whoseelements have a value ranging from 0 to N−1 may be obtained bysequentially subtracting 1 from values of elements in the sequence. Thetwo sequences have same performance, and each can represent thereliability order of the N polarized channels. In the embodiments ofthis application, an example in which the elements in the sequence arearranged in ascending order of the reliability is used for description.It may be understood that a sequence in which the elements are arrangedin descending order of the reliability may be obtained by arranging theelements in the sequence in a reverse order. The two sequences have sameperformance, and each can represent the reliability order of the Npolarized channels.

As shown in FIG. 1, a communications system 100 applied to an embodimentof this application includes a transmit end 101 and a receive end 102.The transmit end 101 may alternatively be referred to as a coding end,and the receive end 102 may alternatively be referred to as a decodingend. The transmit end 101 may be a base station, and the receive end 102is a terminal; or the transmit end 101 is a terminal, and the receiveend 102 is a base station. The base station is an apparatus that isdeployed in a radio access network and that is configured to provide awireless communication function for the terminal. The base station mayinclude various forms of a macro base station, a micro base station, arelay station, or an access point, or the like. The base station may beapplied to systems with different wireless access technologies, such asa Long Term Evolution (LTE) system, or more possible communicationssystems such as a fifth generation (5G) communications system. The basestation may further be another network device that has a function of abase station, and specially, may further be a terminal that serves as abase station in D2D communication. The terminal may include varioushandheld devices, in-vehicle devices, wearable devices, or computingdevices that have a wireless communication function, or anotherprocessing device connected to a wireless modem, various forms of userequipment (UE) or a mobile station (MS), or the like.

Based on a communications system architecture shown in FIG. 1, in theembodiments of this application, a polar coding method may be performedby the transmit end 101. The polar coding method provided in theembodiments of this application is described below in detail.

Based on the communications system architecture shown in FIG. 1, asshown in FIG. 2, a specific procedure of a polar coding method providedin an embodiment of this application is as follows.

Step 201: Determine a sequence used to code to-be-coded bits.

The sequence is used to represent a reliability order of N polarizedchannels, N is a mother code length of a polar code, and N is a positiveinteger power of 2.

Step 202: Perform polar coding on the to-be-coded bits by using thesequence to obtain coded bits.

If a length of the to-be-coded bits is K, the K to-be-coded bits aremapped to K polarized channels in the N polarized channels, andreliability of the K polarized channels is higher than reliability ofremaining N−K polarized channels.

Specifically, sequence numbers of the K polarized channels are selectedin descending order of reliability based on the determined sequence usedto code the to-be-coded bits, and the K to-be-coded bits are placed inthe selected K polarized channels.

In actual application, the sequence used to code the to-be-coded bitsmay be stored in an offline manner. After a transmission parameter (forexample, a code length and a bit rate) is given, an information bit setand a frozen bit set that are used to construct the polar code aredetermined by using the pre-stored sequence. For a specific determiningmethod, refer to the foregoing description of the polar coding process,and details are not described herein again. In addition, in thisembodiment of this application, if the sequence used to code theto-be-coded bits is a sequence with a relatively short code length, thesequence with the relatively short code length may be extracted from astored sequence with a relatively long mother code length based on anesting characteristic of the sequence.

Examples of Q sequences and Z sequences with various mother code lengthsare provided below, and the provided Q sequences and Z sequences bothmay be used to code the to-be-coded bits. In the following example,elements in the sequence are arranged in ascending order of reliabilityof the N polarized channels. L_(n) ^((m)) represents a subsequence inthe sequence, n is a sequence number of the subsequence in the sequence,1≤n≤N, n is a positive integer, m represents a length of an n^(th)subsequence in the sequence, locations of elements in the subsequenceL_(n) ^((m)) are changeable, and sequence numbers at locations outsidethe subsequence in the sequence are fixed. When the locations of theelements in the subsequence L_(n) ^((m)) are exchanged in L_(n) ^((m)),a sequence obtained after the exchange may be obtained based onsequences provided below.

Example 1

(1) When N=64, the sequence is a Q sequence, and the Q sequence mayinclude 11 subsequences whose element locations are changeable. A valueof n ranges from 1 to 11, and the sequence may be:

[1, 2, L₁ ^((m=3)), 17, 33, L₂ ^((m=9)), 21, 35, 25, L₃ ^((m=2)), L₄^((m=2)), L₅ ^((m=3)), 15, 22, L₆ ^((m=3)), 42, 29, L₇ ^((m=2)), 45, L₈^((m=2)), L₉ ^((m=2)), L₁₀ ^((m=2)), 40, 30, L₁₁ ^((m=2)), 46, 52, 47,54, 55, 58, 59, 61, 32, 48, 56, 60, 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=9))=(7, 4, 13, 6, 19, 10, 34, 18, 11); L₃ ^((m=2))=(8,37); L₄ ^((m=2))=(12, 41); L₅ ^((m=3))=(20, 14, 49); L₆ ^((m=6))=(27,36, 39, 23, 38, 26); L₇ ^((m=2))=(50, 43); L₈ ^((m=2))=(16, 51); L₉^((m=2))=(24, 53); L₁₀ ^((m=2))=(57, 28); and L₁₁ ^((m=2))=(44, 31).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 4, 13, 6, 19, 10, 18, 11), 21, 35, 25, (8, 37), (12, 41), (20,14, 49), 15, 22, (27, 36, 39, 23, 38, 26), 42, 29, (50, 43), 45, (16,51), (24, 53), (57, 28), 40, 30, (44, 31), 46, 52, 47, 54, 55, 58, 59,61, 32, 48, 56, 60, 62, 63, 64].

(2) When N=64, the sequence is a Z sequence, and the Z sequence mayinclude two subsequences whose element locations are changeable. A valueof n is 1 or 2. The sequence may be [1, 2, L₁ ^((m=7)), L₂ ^((m=48)) 55,56, 61, 57, 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=7))=(5,9, 3, 11, 8, 20, 4); and L₂ ^((m=48))=(13, 16, 22, 10, 25, 27, 40, 6,15, 12, 24, 17, 28, 32, 42, 19, 34, 29, 45, 36, 47, 49, 58, 7, 14, 18,30, 21, 33, 31, 46, 23, 35, 38, 48, 39, 50, 52, 59, 26, 37, 41, 51, 43,53, 54, 60, 44).

In this example, the Z sequence is specifically: [1, 2, (5, 9, 3, 11, 8,20, 4), (13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28, 32, 42, 19,34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46, 23, 38, 48,39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44), 55, 56, 61, 57, 62,63, 64].

(3) When N=128, the sequence is a Q sequence, and the Q sequence mayinclude 23 subsequences whose element locations are changeable. A valueof n ranges from 1 to 23. The sequence may be: [1, 2, L₁ ^((m=3)), 17,33, L₂ ^((m=10)), 21, 35, 25, L₃ ^((m=4)), L₄ ^((m=2)), L₅ ^((m=4)), L₆^((m=2)), 22, L₇ ^((m=8)), 68, 42, 29, 70, L₈ ^((m=11)), 77, L₉^((m=5)), L₁₀ ^((m=2)), L₁₁ ^((m=7)), 52, L₁₂ ^((m=3)), 54, 78, L₁₃^((m=4)), L₁₄ ^((m=3)), L₁₅ ^((m=3)), 90, L₁₆ ^((m=3)), 103, 106, L₁₇^((m=2)), 107, L₁₈ ^((m=2)), L₁₉ ^((m=2)), L₂₀ ^((m=2)), L₂₁ ^((m=3)),L₂₂ ^((m=4)), 94, 108, 95, 110, 116, 111, 118, 119, 122, L₂₃ ^((m=2)),125, 96, 112, 120, 124, 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=10))=(7, 65, 4, 13, 6, 19, 10, 34, 18, 11); L₃^((m=4))=(66, 8, 37, 67); L₄ ^((m=2))=(12, 41); L₅ ^((m=4))=(20, 14, 69,49); L₆ ^((m=2))=(15, 73); L₇ ^((m=8))=(27, 36, 81, 39, 23, 38, 26, 97);L₈ ^((m=11))=(50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53); L₉^((m=5))=(83, 57, 28, 98, 40); L₁₀ ^((m=2))=(85, 30); L₁₁ ^((m=7))=(44,99, 31, 89, 72, 46, 101); L₁₂ ^((m=3))=(47, 76, 105); L₁₃ ^((m=4))=(55,84, 58, 113); L₁₄ ^((m=3))=(86, 79, 59); L₁₅ ^((m=3))=(100, 87, 61); L₁₆^((m=3))=(102, 91, 32); L₁₇ ^((m=2))=(48, 93); L₁₈ ^((m=2))=(56, 114);L₁₉ ^((m=2))=(80, 109); L₂₀ ^((m=2))=(60, 115); L₂₁ ^((m=3))=(88, 62,117); L₂₂ ^((m=4))=(92, 63, 121, 104); and L₂₃ ^((m=2))=(123, 64).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37, 67),(12, 41), (20, 14, 69, 49), (15, 73), 22, (27, 36, 81, 39, 23, 38, 26,97), 68, 42, 29, 70, (50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53), 77,(83, 57, 28, 98, 40), (85, 30), (44, 99, 31, 89, 72, 46, 101), 52, (47,76, 105), 54, 78, (55, 84, 58, 113), (86, 79, 59), (100, 87, 61), 90,(102, 91, 32), 103, 106, (48, 93), 107, (56, 114), (80, 109), (60, 115),(88, 62, 117), (92, 63, 121, 104), 94, 108, 95, 110, 116, 111, 118, 119,122, (123, 64), 125, 96, 112, 120, 124, 126, 127, 128].

(4) When N=128, the sequence is a Z sequence, and the Z sequence mayinclude one subsequence whose element locations are changeable. A valueof n is 1. The sequence may be: [1, 2, L₁ ^((m=121)), 125, 121, 126,127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=121))=(5,10, 3, 12, 8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33,38, 55, 20, 40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62,26, 43, 48, 65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80,84, 101, 87, 104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47,74, 57, 77, 83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106,95, 110, 112, 122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111,100, 113, 115, 123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118,119).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38, 55, 20,40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26, 43, 48,65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84, 101, 87,104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74, 57, 77,83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95, 110, 112,122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100, 113, 115,123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119), 125, 121,126, 127, 128].

(5) When N=256, the sequence is a Q sequence, and the Q sequence mayinclude 25 subsequences whose element locations are changeable. A valueof n ranges from 1 to 25. The sequence may be: [1, 2, L₁ ^((m=3)), 17,33, L₂ ^((m=11)), 21, 35, 25, L₃ ^((m=28)), 29, L₄ ^((m=18)), L₅^((m=6)), L₆ ^((m=4)), L₇ ^((m=10)), L₈ ^((m=2)), L₉ ^((m=56)), L₁₀^((m=6)), L₁₁ ^((m=9)), L₁₂ ^((m=6)), L₁₃ ^((m=15)), L₁₄ ^((m=8)), L₁₅^((m=6)), L₁₆ ^((m=10)), L₁₇ ^((m=2)), 215, 189, L₁₈ ^((m=4)), 219, L₁₉^((m=5)), L₂₀ ^((m=4)), L₂₁ ^((m=5)), L₂₂ ^((m=3)), L₂₃ ^((m=4)), 222,236, 223, L₂₄ ^((m=5)), L₂₅ ^((m=4)), 253, 224, 240, 248, 252, 254, 255,256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=11))=(7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), L₃^((m=28))=(66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22,131, 27, 36, 81, 137, 39, 23, 38, 26, 97, 68, 42, 145); L₄^((m=18))=(70, 50, 75, 161, 43, 193, 71, 45, 132, 82, 16, 51, 135, 74,24, 53, 134, 77); L₅ ^((m=6))=(83, 138, 57, 28, 98, 40); L₆^((m=4))=(139, 85, 30, 146); L₇ ^((m=10))=(44, 99, 141, 31, 89, 147, 72,162, 46, 101); L₈ ^((m=2))=(149, 52); L₉ ^((m=56))=(47, 76, 105, 165,194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136, 195, 79, 59, 169, 100,140, 197, 87, 177, 61, 90, 102, 148, 142, 143, 91, 201, 32, 103, 106,150, 48, 93, 209, 164, 154, 151, 107, 56, 166, 114, 155, 80, 225, 167,109, 60, 115, 196, 170, 157); L₁₀ ^((m=6))=(88, 62, 117, 171, 198, 178);L₁₁ ^((m=9))=(92, 202, 199, 63, 144, 173, 121, 104, 179); L₁₂ ^((m=6))₁₂=(203, 94, 152, 210, 181, 108) L₁₃ ^((m=15))=(95, 205, 156, 110, 211,185, 116, 168, 158, 226, 111, 213, 118, 172, 227); L₁₄ ^((m=8))=(159,217, 119, 174, 122, 200, 180, 229) L₁₅ ^((m=6))=(175, 123, 64, 233, 204,182); L₁₆ ^((m=10))=(125, 206, 241, 183, 212, 96, 186, 207, 187, 214);L₁₇ ^((m=2))=(228, 112); L₁₈ ^((m=4))=(218, 160, 120, 230); L₁₉^((m=5))=(231, 176, 124, 234, 221); L₂₀ ^((m=4))=(126, 235, 184, 242);L₂₁ ^((m=5))=(188, 208, 237, 127, 243); L₂₂ ^((m=3))=(216, 245, 190);L₂₃ ^((m=4))=(220, 249, 191, 232) L₂₄ ^((m=5))=(238, 244, 239, 246,128); and L₂₅ ^((m=4))=(247, 250, 251, 192).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37,67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27, 36, 81, 137,39, 23, 38, 26, 97, 68, 42, 145), 29, (70, 50, 75, 161, 43, 193, 71, 45,132, 82, 16, 51, 135, 74, 24, 53, 134, 77), (83, 138, 57, 28, 98, 40),(139, 85, 30, 146), (44, 99, 141, 31, 89, 147, 72, 162, 46, 101), (149,52), (47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136,195, 79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142, 143,91, 201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56, 166,114, 155, 80, 225, 167, 109, 60, 115, 196, 170, 157), (88, 62, 117, 171,198, 178), (92, 202, 199, 63, 144, 173, 121, 104, 179), (203, 94, 152,210, 181, 108), (95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111,213, 118, 172, 227), (159, 217, 119, 174, 122, 200, 180, 229), (175,123, 64, 233, 204, 182), (125, 206, 241, 183, 212, 96, 186, 207, 187,214), (228, 112), 215, 189, (218, 160, 120, 230), 219, (231, 176, 124,234, 221), (126, 235, 184, 242), (188, 208, 237, 127, 243), (216, 245,190), (220, 249, 191, 232), 222, 236, 223, (238, 244, 239, 246, 128),(247, 250, 251, 192), 253, 224, 240, 248, 252, 254, 255, 256].

(6) When N=256, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=249)), 253, 249, 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=249))=(5,10, 3, 12, 8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36,43, 65, 21, 45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74,28, 48, 55, 79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71,102, 108, 142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35,64, 53, 92, 68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83,116, 121, 153, 128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160,93, 125, 133, 167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180,185, 213, 159, 187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30,67, 63, 105, 41, 70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89,126, 132, 164, 99, 131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130,94, 135, 140, 175, 109, 145, 150, 181, 158, 186, 191, 217, 114, 152,161, 189, 166, 196, 200, 223, 173, 203, 205, 225, 210, 232, 235, 248,56, 95, 106, 144, 112, 151, 155, 188, 122, 154, 162, 195, 169, 198, 204,226, 129, 165, 172, 201, 179, 206, 209, 230, 184, 211, 215, 233, 220,237, 239, 250, 139, 177, 182, 207, 190, 214, 216, 236, 194, 219, 222,238, 227, 240, 242, 251, 199, 224, 229, 241, 231, 243, 245, 252, 234,246, 247).

In this example, the Q sequence is specifically: [1, 2, (5, 10, 3, 12,8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43, 65, 21,45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28, 48, 55,79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102, 108,142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53, 92,68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121, 153,128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125, 133,167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213, 159,187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105, 41,70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164, 99,131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140, 175,109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166, 196,200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144, 112,151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165, 172,201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250, 139,177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240, 242,251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247), 253, 249,254, 255, 256].

(7) When N=512, the sequence is a Q sequence, and the Q sequence mayinclude 10 subsequences whose element locations are changeable. A valueof n ranges from 1 to 10. The sequence may be: [1, 2, L₁ ^((m=3)), 17,33, L₂ ^((m=11)), L₃ ^((m=4)), L₄ ^((m=419)), L₅ ^((m=6)), L₆ ^((m=28)),L₇ ^((m=23)), L₈ ^((m=5)), 507, L₉ ^((m=2)), L₁₀ ^((m=2)), 508, 510,511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=11))=(7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11); L₃^((m=4))=(257, 21, 35, 25); L₄ ^((m=419))=(66, 8, 37, 67, 130, 12, 41,20, 133, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23,261, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 273, 193,71, 45, 132, 82, 16, 289, 51, 135, 74, 24, 53, 321, 134, 77, 83, 138,57, 28, 260, 98, 40, 385, 139, 85, 30, 262, 146, 44, 99, 141, 31, 89,263, 147, 72, 266, 162, 46, 101, 149, 52, 47, 76, 267, 105, 274, 165,194, 54, 163, 269, 78, 153, 275, 55, 84, 58, 113, 86, 136, 290, 195, 79,291, 59, 277, 169, 100, 140, 197, 87, 177, 61, 90, 281, 102, 148, 293,142, 322, 143, 91, 201, 32, 103, 264, 106, 323, 150, 297, 48, 93, 209,268, 386, 325, 305, 164, 154, 151, 107, 56, 166, 387, 329, 270, 114,155, 80, 225, 167, 276, 109, 271, 60, 115, 196, 170, 157, 88, 62, 278,292, 279, 117, 171, 198, 178, 282, 92, 202, 389, 294, 199, 63, 144, 337,173, 283, 121, 104, 179, 295, 203, 94, 324, 393, 298, 152, 210, 285,181, 108, 95, 205, 299, 353, 326, 156, 110, 401, 306, 301, 211, 185,327, 116, 168, 158, 226, 307, 330, 111, 213, 118, 172, 331, 227, 388,309, 159, 417, 338, 217, 272, 119, 280, 333, 390, 174, 122, 200, 180,229, 339, 313, 391, 175, 394, 284, 123, 64, 341, 449, 354, 395, 233,204, 296, 286, 182, 125, 206, 241, 287, 300, 355, 183, 402, 212, 397,345, 96, 186, 207, 328, 403, 187, 357, 308, 419, 214, 302, 228, 303,361, 112, 418, 215, 405, 310, 189, 450, 332, 218, 160, 120, 230, 334,409, 311, 421, 219, 369, 231, 392, 176, 314, 340, 335, 124, 234, 315,342, 451, 221, 425, 356, 126, 235, 184, 396, 242, 317, 343, 346, 404,288, 398, 453, 433, 188, 358, 208, 237, 347, 362, 127, 243, 406, 216,399, 304, 359, 420, 457, 349, 245, 190, 220, 312, 363, 465, 407, 422,249, 191, 370, 410, 411, 481, 232, 316, 365, 423, 336, 371, 222, 452,426, 413, 454, 318, 236, 344, 373, 223, 427, 434, 238, 348, 244, 455,319, 377, 429, 239, 360, 459, 400, 435, 458, 246, 350, 128, 408, 437,364, 466, 351, 247, 250, 461, 412, 366, 441, 375, 424, 467, 251, 372,192, 482, 414, 367, 469, 374, 428, 415, 253, 483, 430, 224, 456, 473,378, 436, 320, 485); L₅ ^((m=6))=(431, 489, 460, 240, 379, 438); L₆^((m=28))=(462, 381, 248, 442, 352, 470, 439, 463, 252, 497, 468, 368,443, 475, 484, 380, 416, 254, 445, 486, 471, 376, 474, 432, 487, 490,255, 477); L₇ ^((m=23))=(440, 493, 382, 499, 464, 491, 383, 472, 498,444, 501, 446, 447, 476, 488, 478, 494, 505, 256, 492, 479, 384, 500);L₈ ^((m=5))=(503, 495, 502, 448, 506); L₉ ^((m=2))=(480, 509); and L₁₀^((m=2))=(504, 496).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), (257, 21, 35, 25), (66,8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 258, 22, 131, 27,36, 81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50,75, 161, 43, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 24, 53,321, 134, 77, 83, 138, 57, 28, 260, 98, 40, 385, 139, 85, 30, 262, 146,44, 99, 141, 31, 89, 263, 147, 72, 266, 162, 46, 101, 149, 52, 47, 76,267, 105, 274, 165, 194, 54, 163, 269, 78, 153, 275, 55, 84, 58, 113,86, 136, 290, 195, 79, 291, 59, 277, 169, 100, 140, 197, 87, 177, 61,90, 281, 102, 148, 293, 142, 322, 143, 91, 201, 32, 103, 264, 106, 323,150, 297, 48, 93, 209, 268, 386, 325, 305, 164, 154, 151, 107, 56, 166,387, 329, 270, 114, 155, 80, 225, 167, 276, 109, 271, 60, 115, 196, 170,157, 88, 62, 278, 292, 279, 117, 171, 198, 178, 282, 92, 202, 389, 294,199, 63, 144, 337, 173, 283, 121, 104, 179, 295, 203, 94, 324, 393, 298,152, 210, 285, 181, 108, 95, 205, 299, 353, 326, 156, 110, 401, 306,301, 211, 185, 327, 116, 168, 158, 226, 307, 330, 111, 213, 118, 172,331, 227, 388, 309, 159, 417, 338, 217, 272, 119, 280, 333, 390, 174,122, 200, 180, 229, 339, 313, 391, 175, 394, 284, 123, 64, 341, 449,354, 395, 233, 204, 296, 286, 182, 125, 206, 241, 287, 300, 355, 183,402, 212, 397, 345, 96, 186, 207, 328, 403, 187, 357, 308, 419, 214,302, 228, 303, 361, 112, 418, 215, 405, 310, 189, 450, 332, 218, 160,120, 230, 334, 409, 311, 421, 219, 369, 231, 392, 176, 314, 340, 335,124, 234, 315, 342, 451, 221, 425, 356, 126, 235, 184, 396, 242, 317,343, 346, 404, 288, 398, 453, 433, 188, 358, 208, 237, 347, 362, 127,243, 406, 216, 399, 304, 359, 420, 457, 349, 245, 190, 220, 312, 363,465, 407, 422, 249, 191, 370, 410, 411, 481, 232, 316, 365, 423, 336,371, 222, 452, 426, 413, 454, 318, 236, 344, 373, 223, 427, 434, 238,348, 244, 455, 319, 377, 429, 239, 360, 459, 400, 435, 458, 246, 350,128, 408, 437, 364, 466, 351, 247, 250, 461, 412, 366, 441, 375, 424,467, 251, 372, 192, 482, 414, 367, 469, 374, 428, 415, 253, 483, 430,224, 456, 473, 378, 436, 320, 485), (431, 489, 460, 240, 379, 438),(462, 381, 248, 442, 352, 470, 439, 463, 252, 497, 468, 368, 443, 475,484, 380, 416, 254, 445, 486, 471, 376, 474, 432, 487, 490, 255, 477),(440, 493, 382, 499, 464, 491, 383, 472, 498, 444, 501, 446, 447, 476,488, 478, 494, 505, 256, 492, 479, 384, 500), (503, 495, 502, 448, 506),507, (480, 509), (504, 496), 508, 510, 511, 512].

(8) When N=512, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=507)), 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=507))=(5,10, 3, 12, 8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38,46, 72, 22, 49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83,29, 53, 60, 90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164,79, 119, 127, 177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97,36, 71, 58, 105, 76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182,94, 136, 144, 192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147,203, 107, 149, 163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187,237, 248, 309, 202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65,31, 75, 70, 122, 44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139,102, 151, 162, 211, 115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112,160, 109, 165, 173, 230, 129, 180, 188, 238, 200, 252, 260, 319, 134,190, 204, 255, 214, 273, 280, 333, 227, 286, 290, 344, 304, 361, 369,424, 62, 110, 124, 179, 132, 189, 196, 254, 145, 193, 206, 270, 217,275, 287, 346, 155, 212, 226, 282, 236, 294, 301, 353, 246, 307, 315,362, 328, 380, 389, 435, 172, 232, 240, 296, 256, 310, 317, 374, 269,324, 332, 386, 347, 392, 399, 445, 276, 335, 351, 394, 360, 405, 413,450, 368, 414, 422, 456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95,148, 52, 98, 106, 156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184,186, 249, 137, 191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185,140, 195, 205, 271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224,233, 292, 242, 303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440,74, 142, 150, 208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311,322, 378, 199, 245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393,359, 406, 412, 452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349,364, 410, 376, 417, 427, 459, 316, 379, 423, 388, 429, 419, 469, 397,438, 446, 463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259,318, 209, 261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302,352, 366, 408, 312, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314,367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403,439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266,305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455,480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475,491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481,495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493,503, 504, 509, 506).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38, 46, 72, 22,49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83, 29, 53, 60,90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164, 79, 119, 127,177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97, 36, 71, 58, 105,76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182, 94, 136, 144,192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147, 203, 107, 149,163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187, 237, 248, 309,202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65, 31, 75, 70, 122,44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139, 102, 151, 162, 211,115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112, 160, 109, 165, 173,230, 129, 180, 188, 238, 200, 252, 260, 319, 134, 190, 204, 255, 214,273, 280, 333, 227, 286, 290, 344, 304, 361, 369, 424, 62, 110, 124,179, 132, 189, 196, 254, 145, 193, 206, 270, 217, 275, 287, 346, 155,212, 226, 282, 236, 294, 301, 353, 246, 307, 315, 362, 328, 380, 389,435, 172, 232, 240, 296, 256, 310, 317, 374, 269, 324, 332, 386, 347,392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450, 368, 414, 422,456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148, 52, 98, 106,156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186, 249, 137,191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140, 195, 205,271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233, 292, 242,303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440, 74, 142, 150,208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378, 199,245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406, 412,452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314, 367, 377,420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403, 439, 409,447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266, 305, 327,381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455, 480, 365,411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475, 491, 496,505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481, 495, 477,492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493, 503, 504,509, 506), 510, 511, 512].

(9) When N=1024, the sequence is a Q sequence, and the Q sequence mayinclude three subsequences whose element locations are changeable. Avalue of n ranges from 1 to 3. The sequence may be: [1, 2, L₁^((m=3))=17, 33, L₂ ^((m=1011)), L₃ ^((m=7)), 1020, 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=1011))=(7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11,257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49,15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26,97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45,132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57,28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31,89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577, 76, 267,105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525, 84, 58,113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100, 140, 197,87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91, 201,546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209, 268, 386,325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387, 578, 329,549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196, 170,157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178, 282, 92,553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534, 401,306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307, 548,330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394, 284,773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395, 233,204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543, 335,124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621, 466,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374,575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795,865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722,320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240,818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846,921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501, 446,933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638, 908,488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800, 700,494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479, 384,911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923, 875,977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848, 993,448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830, 966,939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751, 872,971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 879,981, 942, 765, 496, 886, 995, 736, 940, 985, 968, 890, 948, 832, 508,943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510, 864, 982,951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511, 766, 957,998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958,976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990,1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960,1021); and L₃ ^((m=2))=(1016, 1008).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66,8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131,27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145,29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51,135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40,385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519,266, 162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54,516, 163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518,195, 79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90,281, 102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106,530, 323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533,164, 154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225,167, 276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292,520, 279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199,524, 63, 144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94,324, 561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770,299, 353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327,539, 116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172,551, 331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550,119, 280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339,657, 313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64,341, 705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286,182, 125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397,345, 587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357,589, 569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650,772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552,651, 120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369,231, 653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659,613, 342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242,558, 661, 617, 317, 343, 346, 779, 564, 404, 288, 398, 453, 675, 559,786, 433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 347, 566, 362,127, 243, 590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457,787, 349, 245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803,407, 681, 422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709,481, 614, 232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612,452, 602, 426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544,373, 655, 223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244,721, 455, 666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459,626, 400, 663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782,898, 408, 667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682,250, 627, 461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629,424, 901, 467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683,414, 604, 794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685,905, 253, 616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836,473, 810, 378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431,607, 717, 489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438,697, 462, 738, 680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352,725, 784, 470, 630, 819, 439, 670, 463, 739, 684, 252, 843, 850, 497,902, 821, 729, 468, 634, 903, 368, 671, 792, 443, 845, 631, 475, 686,851, 484, 692, 712, 380, 866, 796, 416, 825, 961, 741, 254, 906, 635,445, 694, 745, 486, 808, 687, 907, 471, 576, 716, 376, 867, 914, 474,853, 637, 798, 432, 695, 812, 487, 753, 724, 799, 490, 857, 909, 255,718, 608, 931, 477, 698, 726, 915, 440, 820, 840, 869, 493, 719, 699,382, 814, 624, 815, 499, 873, 740, 930, 672, 917, 822, 464, 727, 962,844, 491, 632, 730, 701, 383, 742, 846, 921, 472, 823, 852, 731, 498,881, 743, 444, 904, 688, 826, 501, 446, 933, 847, 636, 746, 827, 733,447, 963, 937, 476, 854, 868, 638, 908, 488, 696, 747, 829, 754, 855,858, 916, 965, 478, 910, 720, 800, 700, 494, 505, 749, 945, 859, 874,639, 755, 256, 969, 870, 492, 479, 384, 911, 816, 918, 728, 871, 702,932, 861, 500, 757, 732, 824, 923, 875, 977, 919, 503, 934, 744, 761,882, 495, 703, 922, 877, 502, 848, 993, 448, 734, 828, 883, 935, 964,506, 938, 748, 856, 925, 735, 830, 966, 939, 885, 507, 750, 946, 860,756, 480, 967, 831, 889, 941, 751, 872, 971, 912, 758, 947, 970, 862,978, 876, 920, 640, 759, 949, 863, 762, 509, 973, 924, 878, 953, 887,936, 979, 763, 504, 884, 704, 994, 926, 879, 981, 942, 765, 496, 927,886, 995, 736, 940, 985, 968, 890, 948, 832, 508, 943, 752, 974, 997,891, 950, 760, 893, 972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009,980, 880, 955, 987, 996, 892, 928, 511, 766, 957, 998, 983, 888, 986,944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512, 1003,895, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012,768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021), (1016,1008), 1020, 1022, 1023, 1024].

(10) When N=1024, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=1010)), 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁^((m=1019))=(5, 11, 3, 13, 8, 25, 4, 16, 29, 12, 34, 37, 71, 6, 18, 14,31, 21, 40, 48, 77, 23, 52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26,51, 47, 89, 30, 56, 63, 97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120,127, 185, 84, 130, 139, 201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59,67, 104, 38, 75, 61, 114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132,146, 206, 101, 150, 159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109,152, 163, 234, 116, 165, 184, 250, 198, 259, 277, 378, 131, 192, 202,269, 213, 280, 296, 395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28,41, 69, 32, 80, 74, 133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95,103, 153, 110, 168, 183, 244, 125, 182, 193, 258, 205, 272, 288, 390,62, 107, 122, 181, 118, 186, 196, 270, 141, 204, 214, 281, 230, 301,314, 411, 147, 217, 235, 306, 248, 338, 348, 433, 266, 357, 364, 452,386, 482, 498, 613, 66, 119, 136, 203, 145, 215, 224, 304, 160, 221,238, 332, 252, 340, 358, 454, 173, 246, 265, 350, 279, 371, 383, 468,293, 389, 406, 484, 426, 518, 536, 641, 195, 273, 284, 373, 307, 396,408, 508, 331, 419, 432, 530, 460, 542, 557, 667, 341, 435, 465, 547,480, 570, 588, 681, 496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45,86, 49, 94, 102, 164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117,126, 197, 140, 209, 212, 297, 151, 218, 231, 317, 247, 337, 345, 445,72, 134, 138, 210, 154, 223, 236, 336, 169, 243, 254, 346, 263, 372,374, 471, 177, 262, 274, 368, 287, 385, 403, 486, 311, 412, 420, 510,439, 528, 551, 654, 79, 157, 167, 240, 176, 256, 267, 359, 189, 276,283, 388, 299, 397, 415, 514, 228, 291, 309, 413, 324, 423, 440, 532,352, 441, 461, 545, 479, 572, 585, 687, 255, 328, 347, 428, 365, 453,473, 559, 377, 463, 488, 581, 512, 597, 621, 708, 407, 500, 516, 611,534, 625, 601, 740, 553, 648, 670, 720, 678, 772, 791, 849, 90, 175,187, 286, 222, 300, 313, 410, 242, 316, 330, 434, 351, 446, 469, 563,261, 349, 362, 444, 384, 467, 492, 577, 398, 502, 504, 595, 524, 618,630, 723, 290, 381, 370, 475, 404, 494, 513, 604, 427, 522, 538, 628,555, 638, 659, 747, 451, 540, 566, 651, 579, 673, 693, 765, 599, 684,711, 802, 730, 807, 814, 878, 326, 387, 425, 520, 447, 526, 549, 643,477, 568, 561, 664, 592, 675, 695, 783, 490, 583, 606, 705, 623, 690,737, 795, 646, 743, 714, 817, 761, 831, 848, 899, 506, 616, 635, 717,656, 733, 750, 822, 662, 754, 787, 847, 769, 836, 871, 938, 701, 799,776, 858, 806, 875, 866, 929, 837, 884, 894, 949, 920, 961, 975, 993,10, 33, 76, 121, 50, 135, 105, 211, 64, 155, 171, 225, 128, 249, 257,333, 87, 166, 142, 237, 180, 260, 292, 361, 178, 298, 268, 382, 312,399, 414, 533, 96, 161, 207, 275, 190, 295, 282, 393, 220, 308, 321,417, 335, 436, 449, 541, 241, 327, 344, 443, 355, 462, 470, 567, 367,481, 499, 587, 509, 614, 626, 738, 113, 188, 199, 302, 245, 315, 334,430, 229, 343, 353, 456, 366, 466, 483, 580, 271, 363, 376, 489, 392,472, 497, 600, 405, 521, 531, 619, 552, 649, 660, 759, 289, 391, 401,519, 422, 507, 537, 634, 438, 544, 571, 650, 582, 669, 685, 774, 476,562, 591, 680, 603, 691, 713, 788, 636, 706, 729, 810, 745, 820, 842,915, 148, 216, 264, 342, 233, 360, 369, 485, 285, 379, 394, 501, 409,525, 535, 627, 310, 402, 421, 511, 437, 554, 564, 652, 455, 550, 578,666, 602, 694, 709, 780, 320, 429, 448, 558, 459, 565, 586, 677, 493,589, 617, 697, 631, 715, 735, 804, 515, 615, 642, 718, 657, 731, 748,823, 674, 762, 771, 835, 790, 855, 872, 931, 325, 458, 487, 593, 505,612, 624, 719, 529, 622, 644, 739, 661, 758, 770, 833, 548, 653, 672,752, 688, 763, 784, 853, 704, 789, 798, 860, 813, 879, 889, 942, 584,676, 696, 778, 726, 792, 801, 868, 732, 811, 824, 886, 838, 895, 904,951, 751, 826, 843, 898, 859, 908, 916, 956, 869, 919, 928, 966, 937,976, 985, 1008, 179, 253, 278, 380, 318, 400, 418, 539, 305, 424, 442,556, 457, 575, 596, 689, 322, 450, 478, 573, 495, 598, 610, 710, 517,620, 639, 722, 655, 746, 753, 834, 329, 474, 491, 608, 523, 637, 629,734, 546, 647, 663, 749, 679, 773, 775, 851, 569, 668, 692, 766, 703,782, 796, 861, 724, 805, 812, 880, 825, 890, 901, 948, 354, 527, 503,645, 560, 671, 665, 767, 594, 683, 699, 786, 712, 793, 809, 876, 607,700, 716, 797, 744, 818, 827, 887, 755, 828, 840, 897, 857, 911, 918,962, 640, 721, 741, 819, 768, 846, 854, 905, 777, 841, 863, 913, 874,923, 934, 969, 800, 870, 881, 930, 893, 940, 925, 980, 902, 946, 954,973, 957, 989, 995, 1013, 375, 576, 543, 682, 605, 702, 707, 803, 632,728, 736, 821, 756, 832, 850, 907, 658, 742, 764, 829, 781, 852, 865,914, 794, 873, 862, 922, 888, 933, 939, 974, 686, 779, 760, 856, 808,867, 882, 926, 816, 885, 892, 943, 903, 936, 950, 982, 839, 896, 909,947, 917, 955, 964, 987, 924, 960, 970, 998, 977, 991, 1001, 1017, 725,785, 815, 883, 830, 891, 900, 945, 845, 910, 906, 958, 921, 952, 965,992, 864, 912, 927, 968, 935, 963, 979, 996, 944, 981, 971, 999, 986,1004, 1006, 1015, 877, 932, 941, 972, 953, 978, 983, 1002, 959, 984,994, 1009, 988, 1003, 1011, 1020, 967, 997, 990, 1007, 1000, 1014, 1010,1019, 1005, 1012, 1016, 1021, 1018).

In this example, the Z sequence is specifically: [1, 2, (5, 11, 3, 13,8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40, 48, 77, 23,52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89, 30, 56, 63,97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185, 84, 130, 139,201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104, 38, 75, 61,114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206, 101, 150,159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163, 234, 116,165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213, 280, 296,395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69, 32, 80, 74,133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153, 110, 168,183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107, 122, 181,118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411, 147, 217,235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482, 498, 613,66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332, 252, 340,358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389, 406, 484,426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508, 331, 419,432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570, 588, 681,496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49, 94, 102,164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197, 140, 209,212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134, 138, 210,154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471, 177, 262,274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528, 551, 654,79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388, 299, 397,415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441, 461, 545,479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559, 377, 463,488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625, 601, 740,553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286, 222, 300,313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349, 362, 444,384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723, 290, 381,370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638, 659, 747,451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802, 730, 807,814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568, 561, 664,592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795, 646, 743,714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733, 750, 822,662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858, 806, 875,866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76, 121, 50,135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166, 142, 237,180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533, 96, 161,207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436, 449, 541,241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587, 509, 614,626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343, 353, 456,366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600, 405, 521,531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507, 537, 634,438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680, 603, 691,713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216, 264, 342,233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627, 310, 402,421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694, 709, 780,320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697, 631, 715,735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762, 771, 835,790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719, 529, 622,644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763, 784, 853,704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778, 726, 792,801, 868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826, 843, 898,859, 908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008, 179, 253,278, 380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575, 596, 689,322, 450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722, 655, 746,753, 834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647, 663, 749,679, 773, 775, 851, 569, 668, 692, 766, 703, 782, 796, 861, 724, 805,812, 880, 825, 890, 901, 948, 354, 527, 503, 645, 560, 671, 665, 767,594, 683, 699, 786, 712, 793, 809, 876, 607, 700, 716, 797, 744, 818,827, 887, 755, 828, 840, 897, 857, 911, 918, 962, 640, 721, 741, 819,768, 846, 854, 905, 777, 841, 863, 913, 874, 923, 934, 969, 800, 870,881, 930, 893, 940, 925, 980, 902, 946, 954, 973, 957, 989, 995, 1013,375, 576, 543, 682, 605, 702, 707, 803, 632, 728, 736, 821, 756, 832,850, 907, 658, 742, 764, 829, 781, 852, 865, 914, 794, 873, 862, 922,888, 933, 939, 974, 686, 779, 760, 856, 808, 867, 882, 926, 816, 885,892, 943, 903, 936, 950, 982, 839, 896, 909, 947, 917, 955, 964, 987,924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785, 815, 883, 830, 891,900, 945, 845, 910, 906, 958, 921, 952, 965, 992, 864, 912, 927, 968,935, 963, 979, 996, 944, 981, 971, 999, 986, 1004, 1006, 1015, 877, 932,941, 972, 953, 978, 983, 1002, 959, 984, 994, 1009, 988, 1003, 1011,1020, 967, 997, 990, 1007, 1000, 1014, 1010, 1019, 1005, 1012, 1016,1021, 1018), 1022, 1023, 1024].

Example 2

(11) When N=64, the sequence is a Q sequence, and the Q sequence mayinclude 12 subsequences whose element locations are changeable. A valueof n ranges from 1 to 12. The sequence may be: [1, 2, L₁ ^((m=3)), 17,L₂ ^((m=10)), 21, 35, 25, L₃ ^((m=2)), L₄ ^((m=2)), L₅ ^((m=3)), 15, 22,L₆ ^((m=6)), L₇ ^((m=2)), L₈ ^((m=5)), L₉ ^((m=2)), L₁₀ ^((m=2)), 40,30, L₁₁ ^((m=2)), 46, 52, 47, 54, 55, 58, 59, L₁₂ ^((m=2)), 48, 56, 60,62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=10))=(33, 7, 4, 13, 6, 19, 10, 34, 18, 11); L₃^((m=2))=(8, 37); L₄ ^((m=2))=(12, 41); L₅ ^((m=3))=20, 14, 49); L₆^((m=6))=(27, 36, 39, 23, 38, 26); L₇ ^((m=2))=(42, 29); L₈^((m=5))=(50, 43, 45, 16, 51); L₉ ^((m=2))(24, 53); L₁₀ ^((m=2))=(57,28); L₁₁ ^((m=2))=(44, 31); and L₁₂ ^((m=2))=(61, 32).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (8, 37), (12, 41),(20, 14, 49), 15, 22, (27, 36, 39, 23, 38, 26), (42, 29), (50, 43, 16,51), (24, 53), (57, 28), 40, 30, (44, 31), 46, 52, 47, 54, 55, 58, 59,(61, 32), 48, 56, 60, 62, 63, 64].

(12) When N=64, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=59)), 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=59))=(5,9, 3, 11, 8, 20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28,32, 42, 19, 34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 23,35, 48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55, 56, 61,57).

In this example, the Z sequence is specifically: [1, 2, (5, 9, 3, 11, 8,20, 4, 13, 16, 22, 10, 25, 27, 6, 15, 12, 24, 17, 28, 32, 42, 19, 34,29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46, 23, 35, 38, 48,50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55, 56, 61, 57), 62, 63,64].

(13) When N=128, the sequence is a Q sequence, and the Q sequence mayinclude 23 (n=23) subsequences whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=3)), 17, L₂ ^((m=11)), 21, 35, 25,L₃ ^((m=4)), L₄ ^((m=2)), L₅ ^((m=4)), L₆ ^((m=2)), 22, L₇ ^((m=9)), L₈^((m=2)), L₉ ^((m=12)), 77, L₁₀ ^((m=5)), L₁₁ ^((m=2)), L₁₂ ^((m=7)),52, L₁₃ ^((m=3)), 54, L₁₄ ^((m=5)), L₁₅ ^((m=3)), L₁₆ ^((m=7)), 103, L₁₇^((m=3)), L₁₈ ^((m=3)), L₁₉ ^((m=2)), L₂₀ ^((m=2)), L₂₁ ^((m=3)), L₂₂^((m=4)), 94, 108, 95, 110, 116, 111, 118, 119, L₂₃ ^((m=5)), 112, 120,124, 126, 127, 128].

In a possible example, L_(n) ^((m)), may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=1))=(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11); L₃^((m=4))=(66, 8, 37, 67); L₄ ^((m=2))=(12, 41); L₅ ^((m=4))=(20, 14, 69,49); L₆ ^((m=2))=(15, 73); L₇ ^((m=9))=(27, 36, 81, 39, 23, 38, 26, 97,68); L₈ ^((m=2))=(42, 29); L₉ ^((m=12))=(70, 50, 75, 43, 71, 45, 82, 16,51, 74, 24, 53); L₁₀ ^((m=5))=(83, 57, 28, 98, 40); L₁₁ ^((m=2))=(85,30); L₁₂ ^((m=7))=(44, 99, 31, 89, 72, 46, 101); L₁₃ ^((m=3))=(47, 76,105); L₁₄ ^((m=s))=(78, 55, 84, 58, 113); L₁₅ ^((m=3))=(86, 79, 59); L₁₆^((m=7))=(100, 87, 61, 90, 102, 91, 32); L₁₇ ^((m=3))=(106, 48, 93); L₁₈^((m=3))=(107, 56, 114); L₁₉ ^((m=2))=(80, 109); L₂₀ ^((m=2))=(60, 115);L₂₁ ^((m=3))=(88, 62, 117); L₂₂ ^((m=4))=(92, 63, 121, 104); and L₂₃^((m=s))=(122, 123, 64, 125, 96).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37, 67),(12, 41), (20, 14, 69, 49), (15, 73), 22, (27, 36, 81, 39, 23, 38, 26,97, 68), (42, 29), (70, 50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53), 77,(83, 57, 28, 98, 40), (85, 30), (44, 99, 31, 89, 72, 46, 101), 52, (47,76, 105), 54, (78, 55, 84, 58, 113), (86, 79, 59), (100, 87, 61, 90,102, 91, 32), 103, (106, 48, 93), (107, 56, 114), (80, 109), (60, 115),(88, 62, 117), (92, 63, 121, 104), 94, 108, 95, 110, 116, 111, 118, 119,(122, 123, 64, 125, 96), 112, 120, 124, 126, 127, 128].

(14) When N=128, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=123)), 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=123))=5,10, 3, 12, 8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33,38, 55, 20, 40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62,26, 43, 48, 65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80,84, 101, 87, 104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47,74, 57, 77, 83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106,95, 110, 112, 122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111,100, 113, 115, 123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119,125, 121).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38, 55, 20,40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26, 43, 48,65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84, 101, 87,104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74, 57, 77,83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95, 110, 112,122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100, 113, 115,123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119, 125, 121),126, 127, 128].

(15) When N=256, the sequence is a Q sequence, and the Q sequence mayinclude 16 subsequences whose element locations are changeable. A valueof n ranges from 1 to 16. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=12)), 21, 35, 25, L₃ ^((m=29)), L₄^((m=28)), L₅ ^((m=12)), L₆ ^((m=32)), L₇ ^((m=54)), L₈ ^((m=9)), L₉^((m=5)), L₁₀ ^((m=4)), L₁₁ ^((m=5)), L₁₂ ^((m=3)), L₁₃ ^((m=4)), 222,236, 223, L₁₄ ^((m=5)), L₁₅ ^((m=4)), L₁₆ ^((m=2)), 240, 248, 252, 254,255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=12))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11); L₃^((m=29))=(66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22,131, 27, 36, 81, 137, 39, 23, 38, 26, 97, 68, 42, 145, 29); L₄^((m=28))=(70, 50, 75, 161, 43, 193, 71, 45, 132, 82, 16, 51, 135, 74,24, 53, 134, 77, 83, 138, 57, 28, 98, 40, 139, 85, 30, 146); L₅^((m=12))=(44, 99, 141, 31, 89, 147, 72, 162, 46, 101, 149, 52); L₆^((m=62))=(47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86,136, 195, 79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142,143, 91, 201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56,166, 114, 155, 80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117,171, 198, 178); L₇ ^((m=54))=(92, 202, 199, 63, 144, 173, 121, 104, 179,203, 94, 152, 210, 181, 108, 95, 205, 156, 110, 211, 185, 116, 168, 158,226, 111, 213, 118, 172, 227, 159, 217, 119, 174, 122, 200, 180, 229,175, 123, 64, 233, 204, 182, 125, 206, 241, 183, 212, 96, 186, 207, 187,214); L₈ ^((m=9))=(228, 112, 215, 189, 218, 160, 120, 230, 219); L₉^((m=5))=(231, 176, 124, 234, 221); L₁₀ ^((m=4))=(126, 235, 184, 242);L₁₁ ^((m=5))=(188, 208, 237, 127, 243); L₁₂ ^((m=3))=(216, 245, 190);L₁₃ ^((m=4))=(220, 249, 191, 232); L₁₄ ^((m=5))=(238, 244, 239, 246,128); L₁₅ ^((m=4))=(247, 250, 251, 192); and L₁₆ ^((m=2))=(253, 224).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37,67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27, 36, 81, 137,39, 23, 38, 26, 97, 68, 42, 145, 29), (70, 50, 75, 161, 43, 193, 71, 45,132, 82, 16, 51, 135, 74, 24, 53, 134, 77, 83, 138, 57, 28, 98, 40, 139,85, 30, 146), (44, 99, 141, 31, 89, 147, 72, 162, 46, 101, 149, 52),(47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136, 195,79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142, 143, 91,201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56, 166, 114,155, 80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117, 171, 198,178), (92, 202, 199, 63, 144, 173, 121, 104, 179, 203, 94, 152, 210,181, 108, 95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111, 213,118, 172, 227, 159, 217, 119, 174, 122, 200, 180, 229, 175, 123, 64,233, 204, 182, 125, 206, 241, 183, 212, 96, 186, 207, 187, 214), (228,112, 215, 189, 218, 160, 120, 230, 219), (231, 176, 124, 234, 221),(126, 235, 184, 242), (188, 208, 237, 127, 243), (216, 245, 190), (220,249, 191, 232), 222, 236, 223, (238, 244, 239, 246, 128), (247, 250,251, 192), (253, 224), 240, 248, 252, 254, 255, 256].

(16) When N=256, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=251)), 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: [L₁^((m=251))=(5, 10, 3, 12, 8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17,13, 29, 19, 36, 43, 65, 21, 45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39,24, 44, 42, 74, 28, 48, 55, 79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96,100, 134, 71, 102, 108, 142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51,57, 85, 35, 64, 53, 92, 68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113,147, 83, 116, 121, 153, 128, 163, 168, 202, 46, 73, 80, 110, 88, 117,124, 160, 93, 125, 133, 167, 141, 171, 178, 208, 103, 136, 143, 174,149, 180, 185, 213, 159, 187, 192, 218, 197, 221, 228, 244, 14, 26, 37,59, 30, 67, 63, 105, 41, 70, 75, 111, 81, 119, 120, 157, 49, 78, 84,118, 89, 126, 132, 164, 99, 131, 137, 170, 146, 176, 183, 212, 54, 86,97, 130, 94, 135, 140, 175, 109, 145, 150, 181, 158, 186, 191, 217, 114,152, 161, 189, 166, 196, 200, 223, 173, 203, 205, 225, 210, 232, 235,248, 56, 95, 106, 144, 112, 151, 155, 188, 122, 154, 162, 195, 169, 198,204, 226, 129, 165, 172, 201, 179, 206, 209, 230, 184, 211, 215, 233,220, 237, 239, 250, 139, 177, 182, 207, 190, 214, 216, 236, 194, 219,222, 238, 227, 240, 242, 251, 199, 224, 229, 241, 231, 243, 245, 252,234, 246, 247, 253, 249)].

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43, 65, 21,45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28, 48, 55,79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102, 108,142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53, 92,68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121, 153,128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125, 133,167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213, 159,187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105, 41,70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164, 99,131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140, 175,109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166, 196,200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144, 112,151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165, 172,201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250, 139,177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240, 242,251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247, 253, 249),254, 255, 256].

(17) When N=512, the sequence is a Q sequence, and the Q sequence mayinclude six subsequences whose element locations are changeable. A valueof n ranges from 1 to 6. The sequence may be: [1, 2, L₁ ^((m=3)), 17. L₂^((m=441)). L₃ ^((m=28)). L₄ ^((m=28)), 507, L₅ ^((m=2)), L₆ ^((m=2)),508, 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=441))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257,21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73,258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265,42, 145, 29, 70, 50, 75, 161, 43, 273, 193, 71, 45, 132, 82, 16, 289,51, 135, 74, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 98, 40, 385,139, 85, 30, 262, 146, 44, 99, 141, 31, 89, 263, 147, 72, 266, 162, 46,101, 149, 52, 47, 76, 267, 105, 274, 165, 194, 54, 163, 269, 78, 153,275, 55, 84, 58, 113, 86, 136, 290, 195, 79, 291, 59, 277, 169, 100,140, 197, 87, 177, 61, 90, 281, 102, 148, 293, 142, 322, 143, 91, 201,32, 103, 264, 106, 323, 150, 297, 48, 93, 209, 268, 386, 325, 305, 164,154, 151, 107, 56, 166, 387, 329, 270, 114, 155, 80, 225, 167, 276, 109,271, 60, 115, 196, 170, 157, 88, 62, 278, 292, 279, 117, 171, 198, 178,282, 92, 202, 389, 294, 199, 63, 144, 337, 173, 283, 121, 104, 179, 295,203, 94, 324, 393, 298, 152, 210, 285, 181, 108, 95, 205, 299, 353, 326,156, 110, 401, 306, 301, 211, 185, 327, 116, 168, 158, 226, 307, 330,111, 213, 118, 172, 331, 227, 388, 309, 159, 417, 338, 217, 272, 119,280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 175, 394, 284,123, 64, 341, 449, 354, 395, 233, 204, 296, 286, 182, 125, 206, 241,287, 300, 355, 183, 402, 212, 397, 345, 96, 186, 207, 328, 403, 187,357, 308, 419, 214, 302, 228, 303, 361, 112, 418, 215, 405, 310, 189,450, 332, 218, 160, 120, 230, 334, 409, 311, 421, 219, 369, 231, 392,176, 314, 340, 335, 124, 234, 315, 342, 451, 221, 425, 356, 126, 235,184, 396, 242, 317, 343, 346, 404, 288, 398, 453, 433, 188, 358, 208,237, 347, 362, 127, 243, 406, 216, 399, 304, 359, 420, 457, 349, 245,190, 220, 312, 363, 465, 407, 422, 249, 191, 370, 410, 411, 481, 232,316, 365, 423, 336, 371, 222, 452, 426, 413, 454, 318, 236, 344, 373,223, 427, 434, 238, 348, 244, 455, 319, 377, 429, 239, 360, 459, 400,435, 458, 246, 350, 128, 408, 437, 364, 466, 351, 247, 250, 461, 412,366, 441, 375, 424, 467, 251, 372, 192, 482, 414, 367, 469, 374, 428,415, 253, 483, 430, 224, 456, 473, 378, 436, 320, 485, 431, 489, 460,240, 379, 438); L₃ ^((m=28))=(462, 381, 248, 442, 352, 470, 439, 463,252, 497, 468, 368, 443, 475, 484, 380, 416, 254, 445, 486, 471, 376,474, 432, 487, 490, 255, 477); L₄ ^((m=28))=(440, 493, 382, 499, 464,491, 383, 472, 498, 444, 501, 446, 447, 476, 488, 478, 494, 505, 256,492, 479, 384, 500, 503, 495, 502, 448, 506); L₅ ^((m=2))=(480, 509);and L₆ ^((m=2))=(504, 496).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66, 8,37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36,81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50, 75,161, 43, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 24, 53, 321,134, 77, 83, 138, 57, 28, 260, 98, 40, 385, 139, 85, 30, 262, 146, 44,99, 141, 31, 89, 263, 147, 72, 266, 162, 46, 101, 149, 52, 47, 76, 267,105, 274, 165, 194, 54, 163, 269, 78, 153, 275, 55, 84, 58, 113, 86,136, 290, 195, 79, 291, 59, 277, 169, 100, 140, 197, 87, 177, 61, 90,281, 102, 148, 293, 142, 322, 143, 91, 201, 32, 103, 264, 106, 323, 150,297, 48, 93, 209, 268, 386, 325, 305, 164, 154, 151, 107, 56, 166, 387,329, 270, 114, 155, 80, 225, 167, 276, 109, 271, 60, 115, 196, 170, 157,88, 62, 278, 292, 279, 117, 171, 198, 178, 282, 92, 202, 389, 294, 199,63, 144, 337, 173, 283, 121, 104, 179, 295, 203, 94, 324, 393, 298, 152,210, 285, 181, 108, 95, 205, 299, 353, 326, 156, 110, 401, 306, 301,211, 185, 327, 116, 168, 158, 226, 307, 330, 111, 213, 118, 172, 331,227, 388, 309, 159, 417, 338, 217, 272, 119, 280, 333, 390, 174, 122,200, 180, 229, 339, 313, 391, 175, 394, 284, 123, 64, 341, 449, 354,395, 233, 204, 296, 286, 182, 125, 206, 241, 287, 300, 355, 183, 402,212, 397, 345, 96, 186, 207, 328, 403, 187, 357, 308, 419, 214, 302,228, 303, 361, 112, 418, 215, 405, 310, 189, 450, 332, 218, 160, 120,230, 334, 409, 311, 421, 219, 369, 231, 392, 176, 314, 340, 335, 124,234, 315, 342, 451, 221, 425, 356, 126, 235, 184, 396, 242, 317, 343,346, 404, 288, 398, 453, 433, 188, 358, 208, 237, 347, 362, 127, 243,406, 216, 399, 304, 359, 420, 457, 349, 245, 190, 220, 312, 363, 465,407, 422, 249, 191, 370, 410, 411, 481, 232, 316, 365, 423, 336, 371,222, 452, 426, 413, 454, 318, 236, 344, 373, 223, 427, 434, 238, 348,244, 455, 319, 377, 429, 239, 360, 459, 400, 435, 458, 246, 350, 128,408, 437, 364, 466, 351, 247, 250, 461, 412, 366, 441, 375, 424, 467,251, 372, 192, 482, 414, 367, 469, 374, 428, 415, 253, 483, 430, 224,456, 473, 378, 436, 320, 485, 431, 489, 460, 240, 379, 438), (462, 381,248, 442, 352, 470, 439, 463, 252, 497, 468, 368, 443, 475, 484, 380,416, 254, 445, 486, 471, 376, 474, 432, 487, 490, 255, 477), (440, 493,382, 499, 464, 491, 383, 472, 498, 444, 501, 446, 447, 476, 488, 478,494, 505, 256, 492, 479, 384, 500, 503, 495, 502, 448, 506), 507, (480,509), (504, 496), 508, 510, 511, 512].

(18) When N=512, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=507)), 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=507))=(5,10, 3, 12, 8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38,46, 72, 22, 49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83,29, 53, 60, 90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164,79, 119, 127, 177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97,36, 71, 58, 105, 76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182,94, 136, 144, 192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147,203, 107, 149, 163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187,237, 248, 309, 202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65,31, 75, 70, 122, 44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139,102, 151, 162, 211, 115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112,160, 109, 165, 173, 230, 129, 180, 188, 238, 200, 252, 260, 319, 134,190, 204, 255, 214, 273, 280, 333, 227, 286, 290, 344, 304, 361, 369,424, 62, 110, 124, 179, 132, 189, 196, 254, 145, 193, 206, 270, 217,275, 287, 346, 155, 212, 226, 282, 236, 294, 301, 353, 246, 307, 315,362, 328, 380, 389, 435, 172, 232, 240, 296, 256, 310, 317, 374, 269,324, 332, 386, 347, 392, 399, 445, 276, 335, 351, 394, 360, 405, 413,450, 368, 414, 422, 456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95,148, 52, 98, 106, 156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184,186, 249, 137, 191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185,140, 195, 205, 271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224,233, 292, 242, 303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440,74, 142, 150, 208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311,322, 378, 199, 245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393,359, 406, 412, 452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349,364, 410, 376, 417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469,397, 438, 446, 463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251,259, 318, 209, 261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339,302, 352, 366, 408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300,293, 357, 314, 367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471,343, 391, 403, 439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487,488, 502, 266, 305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444,415, 448, 455, 480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470,461, 489, 475, 491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490,443, 473, 481, 495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501,499, 507, 493, 503, 504, 509, 506).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38, 46, 72, 22,49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83, 29, 53, 60,90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164, 79, 119, 127,177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97, 36, 71, 58, 105,76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182, 94, 136, 144,192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147, 203, 107, 149,163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187, 237, 248, 309,202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65, 31, 75, 70, 122,44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139, 102, 151, 162, 211,115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112, 160, 109, 165, 173,230, 129, 180, 188, 238, 200, 252, 260, 319, 134, 190, 204, 255, 214,273, 280, 333, 227, 286, 290, 344, 304, 361, 369, 424, 62, 110, 124,179, 132, 189, 196, 254, 145, 193, 206, 270, 217, 275, 287, 346, 155,212, 226, 282, 236, 294, 301, 353, 246, 307, 315, 362, 328, 380, 389,435, 172, 232, 240, 296, 256, 310, 317, 374, 269, 324, 332, 386, 347,392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450, 368, 414, 422,456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148, 52, 98, 106,156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186, 249, 137,191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140, 195, 205,271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233, 292, 242,303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440, 74, 142, 150,208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378, 199,245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406, 412,452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314,367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403,439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266,305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455,480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475,491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481,495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493,503, 504, 509, 506), 510, 511, 512].

(19) When N=1024, the sequence is a Q sequence, and the Q sequence mayinclude three subsequences whose element locations are changeable. Avalue of n ranges from 1 to 3. The sequence may be: [1, 2, L₁ ^((m=3)),17, L₂ ^((m=1012)), L₃ ^((m=3)), 1020, 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^(m=1012))=(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11,257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49,15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26,97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45,132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57,28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31,89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577, 76, 267,105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525, 84, 58,113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100, 140, 197,87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91, 201,546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209, 268, 386,325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387, 578, 329,549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196, 170,157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178, 282, 92,553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534, 401,306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307, 548,330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394, 284,773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395, 233,204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543, 335,124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621, 466,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374,575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795,865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722,320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240,818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846,921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501, 446,933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638, 908,488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800, 700,494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479, 384,911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923, 875,977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848, 993,448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830, 966,939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751, 872,971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926,879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948,832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510,864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511,766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894,1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000,1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992,1019, 960, 1021); and L₃ ^((m=2))=(1016, 1008).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66,8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131,27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145,29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51,135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40,385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519,266, 162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54,516, 163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518,195, 79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90,281, 102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106,530, 323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533,164, 154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225,167, 276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292,520, 279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199,524, 63, 144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94,324, 561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770,299, 353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327,539, 116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172,551, 331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550,119, 280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339,657, 313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64,341, 705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286,182, 125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397,345, 587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357,589, 569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650,772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552,651, 120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369,231, 653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659,613, 342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242,558, 661, 617, 317, 343, 779, 564, 404, 288, 398, 453, 675, 559, 786,433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 566, 362, 127, 243,590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457, 787, 349,245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803, 407, 681,422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709, 481, 614,232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612, 452, 602,426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544, 373, 655,223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244, 721, 455,666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459, 626, 400,663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782, 898, 408,667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682, 250, 627,461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629, 424, 901,467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683, 414, 604,794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685, 905, 253,616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836, 473, 810,378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431, 607, 717,489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438, 697, 462,680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352, 725, 784, 470,630, 819, 439, 670, 463, 684, 252, 843, 850, 497, 902, 821, 729, 468,634, 903, 368, 671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712,380, 866, 796, 416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486,808, 687, 907, 471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432,695, 812, 487, 753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477,698, 726, 915, 440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815,499, 873, 740, 930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730,701, 383, 742, 846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904,688, 826, 501, 446, 933, 847, 636, 746, 827, 733, 447, 963, 937, 476,854, 868, 638, 908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478,910, 720, 800, 700, 494, 505, 749, 945, 859, 874, 639, 755, 256, 969,870, 492, 479, 384, 911, 816, 918, 728, 871, 702, 932, 861, 500, 757,732, 824, 923, 875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922,877, 502, 848, 993, 448, 734, 828, 883, 935, 964, 506, 938, 748, 856,925, 735, 830, 966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831,889, 941, 751, 872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640,759, 949, 863, 762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504,884, 704, 994, 926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940,985, 968, 890, 948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893,972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987,996, 892, 928, 511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767,989, 952, 1005, 894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956,988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007,1018, 896, 1014, 992, 1019, 960, 1021), (1016, 1008), 1020, 1022, 1023,1024].

(20) When N=1024, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=1019), 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁^((m=1019))=(5, 11, 3, 13, 8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18,14, 31, 21, 40, 48, 77, 23, 52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43,26, 51, 47, 89, 30, 56, 63, 97, 68, 108, 112, 170, 36, 60, 73, 111, 78,120, 127, 185, 84, 130, 139, 201, 149, 208, 226, 323, 9, 24, 27, 54, 35,59, 67, 104, 38, 75, 61, 114, 81, 124, 137, 194, 44, 70, 82, 129, 92,132, 146, 206, 101, 150, 159, 219, 172, 239, 251, 356, 53, 88, 98, 143,109, 152, 163, 234, 116, 165, 184, 250, 198, 259, 277, 378, 131, 192,202, 269, 213, 280, 296, 395, 232, 303, 319, 416, 339, 431, 464, 574,15, 28, 41, 69, 32, 80, 74, 133, 46, 83, 91, 144, 99, 156, 158, 227, 57,95, 103, 153, 110, 168, 183, 244, 125, 182, 193, 258, 205, 272, 288,390, 62, 107, 122, 181, 118, 186, 196, 270, 141, 204, 214, 281, 230,301, 314, 411, 147, 217, 235, 306, 248, 338, 348, 433, 266, 357, 364,452, 386, 482, 498, 613, 66, 119, 136, 203, 145, 215, 224, 304, 160,221, 238, 332, 252, 340, 358, 454, 173, 246, 265, 350, 279, 371, 383,468, 293, 389, 406, 484, 426, 518, 536, 641, 195, 273, 284, 373, 307,396, 408, 508, 331, 419, 432, 530, 460, 542, 557, 667, 341, 435, 465,547, 480, 570, 588, 681, 496, 590, 609, 698, 633, 727, 757, 844, 20, 39,45, 86, 49, 94, 102, 164, 55, 106, 115, 174, 123, 191, 200, 294, 65,117, 126, 197, 140, 209, 212, 297, 151, 218, 231, 317, 247, 337, 345,445, 72, 134, 138, 210, 154, 223, 236, 336, 169, 243, 254, 346, 263,372, 374, 471, 177, 262, 274, 368, 287, 385, 403, 486, 311, 412, 420,510, 439, 528, 551, 654, 79, 157, 167, 240, 176, 256, 267, 359, 189,276, 283, 388, 299, 397, 415, 514, 228, 291, 309, 413, 324, 423, 440,532, 352, 441, 461, 545, 479, 572, 585, 687, 255, 328, 347, 428, 365,453, 473, 559, 377, 463, 488, 581, 512, 597, 621, 708, 407, 500, 516,611, 534, 625, 601, 740, 553, 648, 670, 720, 678, 772, 791, 849, 90,175, 187, 286, 222, 300, 313, 410, 242, 316, 330, 434, 351, 446, 469,563, 261, 349, 362, 444, 384, 467, 492, 577, 398, 502, 504, 595, 524,618, 630, 723, 290, 381, 370, 475, 404, 494, 513, 604, 427, 522, 538,628, 555, 638, 659, 747, 451, 540, 566, 651, 579, 673, 693, 765, 599,684, 711, 802, 730, 807, 814, 878, 326, 387, 425, 520, 447, 526, 549,643, 477, 568, 561, 664, 592, 675, 695, 783, 490, 583, 606, 705, 623,690, 737, 795, 646, 743, 714, 817, 761, 831, 848, 899, 506, 616, 635,717, 656, 733, 750, 822, 662, 754, 787, 847, 769, 836, 871, 938, 701,799, 776, 858, 806, 875, 866, 929, 837, 884, 894, 949, 920, 961, 975,993, 10, 33, 76, 121, 50, 135, 105, 211, 64, 155, 171, 225, 128, 249,257, 333, 87, 166, 142, 237, 180, 260, 292, 361, 178, 298, 268, 382,312, 399, 414, 533, 96, 161, 207, 275, 190, 295, 282, 393, 220, 308,321, 417, 335, 436, 449, 541, 241, 327, 344, 443, 355, 462, 470, 567,367, 481, 499, 587, 509, 614, 626, 738, 113, 188, 199, 302, 245, 315,334, 430, 229, 343, 353, 456, 366, 466, 483, 580, 271, 363, 376, 489,392, 472, 497, 600, 405, 521, 531, 619, 552, 649, 660, 759, 289, 391,401, 519, 422, 507, 537, 634, 438, 544, 571, 650, 582, 669, 685, 774,476, 562, 591, 680, 603, 691, 713, 788, 636, 706, 729, 810, 745, 820,842, 915, 148, 216, 264, 342, 233, 360, 369, 485, 285, 379, 394, 501,409, 525, 535, 627, 310, 402, 421, 511, 437, 554, 564, 652, 455, 550,578, 666, 602, 694, 709, 780, 320, 429, 448, 558, 459, 565, 586, 677,493, 589, 617, 697, 631, 715, 735, 804, 515, 615, 642, 718, 657, 731,748, 823, 674, 762, 771, 835, 790, 855, 872, 931, 325, 458, 487, 593,505, 612, 624, 719, 529, 622, 644, 739, 661, 758, 770, 833, 548, 653,672, 752, 688, 763, 784, 853, 704, 789, 798, 860, 813, 879, 889, 942,584, 676, 696, 778, 726, 792, 801, 868, 732, 811, 824, 886, 838, 895,904, 951, 751, 826, 843, 898, 859, 908, 916, 956, 869, 919, 928, 966,937, 976, 985, 1008, 179, 253, 278, 380, 318, 400, 418, 539, 305, 424,442, 556, 457, 575, 596, 689, 322, 450, 478, 573, 495, 598, 610, 710,517, 620, 639, 722, 655, 746, 753, 834, 329, 474, 491, 608, 523, 637,629, 734, 546, 647, 663, 749, 679, 773, 775, 851, 569, 668, 692, 703,782, 796, 861, 724, 805, 812, 880, 825, 890, 901, 948, 354, 527, 503,645, 560, 671, 665, 594, 683, 699, 786, 712, 793, 809, 876, 607, 700,716, 797, 744, 818, 827, 887, 755, 828, 840, 897, 857, 911, 918, 962,640, 721, 741, 819, 768, 846, 854, 905, 777, 841, 863, 913, 874, 923,934, 969, 800, 870, 881, 930, 893, 940, 925, 980, 902, 946, 954, 973,957, 989, 995, 1013, 375, 576, 543, 682, 605, 702, 707, 803, 632, 728,736, 821, 756, 832, 850, 907, 658, 742, 764, 829, 781, 852, 865, 914,794, 873, 862, 922, 888, 933, 939, 974, 686, 779, 760, 856, 808, 867,882, 926, 816, 885, 892, 943, 903, 936, 950, 982, 839, 896, 909, 947,917, 955, 964, 987, 924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785,815, 883, 830, 891, 900, 945, 845, 910, 906, 958, 921, 952, 965, 992,864, 912, 927, 968, 935, 963, 979, 996, 944, 981, 971, 999, 986, 1004,1006, 1015, 877, 932, 941, 972, 953, 978, 983, 1002, 959, 984, 994,1009, 988, 1003, 1011, 1020, 967, 997, 990, 1007, 1000, 1014, 1010,1019, 1005, 1012, 1016, 1021, 1018).

In this example, the Z sequence is specifically: [1, 2, (5, 11, 3, 13,8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40, 48, 77, 23,52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89, 30, 56, 63,97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185, 84, 130, 139,201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104, 38, 75, 61,114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206, 101, 150,159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163, 234, 116,165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213, 280, 296,395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69, 32, 80, 74,133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153, 110, 168,183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107, 122, 181,118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411, 147, 217,235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482, 498, 613,66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332, 252, 340,358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389, 406, 484,426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508, 331, 419,432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570, 588, 681,496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49, 94, 102,164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197, 140, 209,212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134, 138, 210,154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471, 177, 262,274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528, 551, 654,79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388, 299, 397,415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441, 461, 545,479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559, 377, 463,488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625, 601, 740,553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286, 222, 300,313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349, 362, 444,384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723, 290, 381,370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638, 659, 747,451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802, 730, 807,814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568, 561, 664,592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795, 646, 743,714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733, 750, 822,662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858, 806, 875,866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76, 121, 50,135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166, 142, 237,180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533, 96, 161,207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436, 449, 541,241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587, 509, 614,626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343, 353, 456,366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600, 405, 521,531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507, 537, 634,438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680, 603, 691,713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216, 264, 342,233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627, 310, 402,421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694, 709, 780,320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697, 631, 715,735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762, 771, 835,790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719, 529, 622,644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763, 784, 853,704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778, 726, 792,868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826, 843, 898, 859,908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008, 179, 253, 278,380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575, 596, 689, 322,450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722, 655, 746, 753,834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647, 663, 749, 679,773, 775, 851, 569, 668, 692, 703, 782, 796, 861, 724, 805, 812, 880,825, 890, 901, 948, 354, 527, 503, 645, 560, 671, 665, 594, 683, 699,786, 712, 793, 809, 876, 607, 700, 716, 797, 744, 818, 827, 887, 755,828, 840, 897, 857, 911, 918, 962, 640, 721, 741, 819, 768, 846, 854,905, 777, 841, 863, 913, 874, 923, 934, 969, 870, 881, 930, 893, 940,925, 980, 902, 946, 954, 973, 957, 989, 995, 1013, 375, 576, 543, 682,605, 702, 707, 803, 632, 728, 736, 821, 756, 832, 850, 907, 658, 742,764, 829, 781, 852, 865, 914, 794, 873, 862, 922, 888, 933, 939, 974,686, 779, 760, 856, 808, 867, 882, 926, 816, 885, 892, 943, 903, 936,950, 982, 839, 896, 909, 947, 917, 955, 964, 987, 924, 960, 970, 998,977, 991, 1001, 1017, 725, 785, 815, 883, 830, 891, 900, 945, 845, 910,906, 958, 921, 952, 965, 992, 864, 912, 927, 968, 935, 963, 979, 996,944, 981, 971, 999, 986, 1004, 1006, 1015, 877, 932, 941, 972, 953, 978,983, 1002, 959, 984, 994, 1009, 988, 1003, 1011, 1020, 967, 997, 990,1007, 1000, 1014, 1010, 1019, 1005, 1012, 1016, 1021, 1018), 1022, 1023,1024].

Example 3

(21) When N=64, the sequence is a Q sequence, and the Q sequence mayinclude 11 subsequences whose element locations are changeable. A valueof n ranges from 1 to 11. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=15)), L₃ ^((m=2)), L₄ ^((m=3)), 15, 22,L₅ ^((m=6)), L₆ ^((m=2)), L₇ ^((m=5)), L₈ ^((m=2)), L₉ ^((m=3)), 30, L₁₀^((m=2)), 46, 52, 47, 54, 55, 58, 59, L₁₁ ^((m=2)), 48, 56, 60, 62, 63,64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=15))=(33, 7, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25, 8,37); L₃ ^((m=2))=(12, 41); L₄ ^((m=3))=(20, 14, 49); L₅ ^((m=6))=(27,36, 39, 23, 38, 26); L₆ ^((m=2))=(42, 29); L₇ ^((m=5))=(50, 43, 45, 16,51); L₈ ^((m=2))=(24, 53); L₉ ^((m=3))=(57, 28, 40); L₁₀ ^((m=2))=(44,31); and L₁₁ ^((m=2))=(61, 32).

N=64, and locations of elements in the subsequence L₁ ^((m=3)) in the Qsequence may be exchanged in the subsequence L₁ ^((m=3)), for example,may be (5, 9, 3), and may be exchanged to (3, 9, 5) or (5, 3, 9).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25, 8, 37), (12, 41), (20,14, 49), 15, 22, (27, 36, 39, 23, 38, 26), (42, 29), (50, 43, 45, 16,51), (24, 53), (57, 28, 40), 30, (44, 31), 46, 52, 47, 54, 55, 58, 59,(61, 32), 48, 56, 60, 62, 63, 64]. A set in parentheses is thesubsequence L_(n) ^((m)).

(22) When N=64, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be:

[1, 2, L₁ ^((m=59)), 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=59))=(5,9, 3, 11, 8, 20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28,32, 42, 19, 34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46,23, 35, 38, 48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55,56, 61, 57). Locations of elements in L₁ ^((m=59)) may be exchanged inthe subsequence.

In this example, the Z sequence is specifically: [1, 2, (5, 9, 3, 11, 8,20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28, 32, 42, 19,34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46, 23, 35, 38,48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55, 56, 61, 57),62, 63, 64].

(23) When N=128, the sequence is a Q sequence, and the Q sequence mayinclude 17 subsequences whose element locations are changeable. Avalueof n ranges from 1 to 17. The sequence may be:

[1, 2 L₁ ^((m=3)), 17, L₂ ^((m=20)), L₃ ^((m=6)), 22 L₄ ^((m=11)), L₅^((m=12)), 77, L₆ ^((m=7)), L₇ ^((m=7)), 52 L₈ ^((m=4)), L₉ ^((m=15)),L₁₀ ^((m=4)), L₁₁ ^((m=3)), L₁₂ ^((m=2)), L₁₃ ^((m=2)), L₁₄ ^((m=3)),L₁₅ ^((m=4)), L₁₆ ^((m=2)), 110, 116, 111, 118 L₁₇ ^((m=6)), 112, 120,124, 126, 127, 128].

In a possible example L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5, 9,3); L₂ ^((m=20))=(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25,66, 8, 37, 67, 12, 41); L₃ ^((m=6))=(20, 14, 69, 49, 15, 73); L₄^((m=11))=(27, 36, 81, 39, 23, 38, 26, 97, 68, 42, 29); L₂^((m=12))=(70, 50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53); L₆^((m=7))=(83, 57, 28, 98, 40, 85, 30); L₇ ^((m=7))=(44, 99, 31, 89, 72,46, 101); L₈ ^((m=4))=(47, 76, 105, 54); L₉ ^((m=15))=(78, 55, 84, 58,113, 86, 79, 59, 100, 87, 61, 90, 102, 91, 32); L₁₀ ^((m=4))=(103, 106,48, 93); L₁₁ ^((m=3))=(107, 56, 114); L₁₂ ^((m=2))=(80, 109); L₁₃^((m=2))=(60, 115); L₁₄ ^((m=3))=(88, 62, 117); L₁₅ ^((m=4))=(92, 63,121, 104); L₁₆ ^((m=2))=(108, 95); and L₁₇ ^((m=6))=(119, 122, 123, 64,125, 96).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25, 66, 8, 37, 67, 12,41), (20, 14, 69, 49, 15, 73), 22, (27, 36, 81, 39, 23, 38, 26, 97, 68,42, 29), (70, 50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53), 77, (83, 57,28, 98, 40, 85, 30), (44, 99, 31, 89, 72, 46, 101), 52, (47, 76, 105,54), (78, 55, 84, 58, 113, 86, 79, 59, 100, 87, 61, 90, 102, 91, 32),(103, 106, 48, 93), (107, 56, 114), (80, 109), (60, 115), (88, 62, 117),(92, 63, 121, 104), 94, (108, 95), 110, 116, 111, 118, (119, 122, 123,64, 125, 96), 112, 120, 124, 126, 127, 128].

(34) When N=128, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be:

[1, 2, L₁ ^((m=123)), 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=123))=(5,10, 3, 12, 8, 22, 4, 14, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38,55, 20, 40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26,43, 48, 65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84,101, 87, 104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74,57, 77, 83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95,110, 112, 122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100,113, 115, 123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119, 125,121).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38, 55, 20,40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26, 43, 48,65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84, 101, 87,104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74, 57, 77,83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95, 110, 112,122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100, 113, 115,123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119, 125, 121),126, 127, 128].

(25) When N=256, the sequence is a Q sequence, and the Q sequence mayinclude nine subsequences whose element locations are changeable. Avalue of n ranges from 1 to 9. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=209)), L₃ ^((m=14)), L₄ ^((m=3)), L₅^((m=4)), 222, L₆ ^((m=2)), L₇ ^((m=5)), L₈ ^((m=4)), L₉ ^((m=2)), 240,248, 252, 254, 255, 256].

In a possible example, may be as follows: L₁ ^((m=3))=(5, 9, 3); L₂^((m=209))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 21, 35, 25,66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27,36, 81, 137, 39, 23, 38, 26, 97, 68, 42, 145, 29, 70, 50, 75, 161, 43,193, 71, 45, 132, 82, 16, 51, 135, 74, 24, 53, 134, 77, 83, 138, 57, 28,98, 40, 139, 85, 30, 146, 44, 99, 141, 31, 89, 147, 72, 162, 46, 101,149, 52, 47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86,136, 195, 79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142,143, 91, 201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56,166, 114, 155, 80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117,171, 198, 178, 92, 202, 199, 63, 144, 173, 121, 104, 179, 203, 94, 152,210, 181, 108, 95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111,213, 118, 172, 227, 159, 217, 119, 174, 122, 200, 180, 229, 175, 123,64, 233, 204, 182, 125, 206, 241, 183, 212, 96, 186, 207, 187, 214, 228,112, 215, 189, 218, 160, 120, 230, 219); L₃ ^((m=14))=(231, 176, 124,234, 221, 126, 235, 184, 242, 188, 208, 237, 127, 243); L₄^((m=3))=(216, 245, 190); L₅ ^((m=4))=(220, 249, 191, 232); L₆^((m=2))=(236, 223); L₇ ^((m=5))=(238, 244, 239, 246, 128); L₈^((m=4))=(247, 250, 251, 192); and L₉ ^((m=2))=(253, 224).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 21, 35, 25, 66, 8, 37,67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27, 36, 81, 137,39, 23, 38, 26, 97, 68, 42, 145, 29, 70, 50, 75, 161, 43, 193, 71, 45,132, 82, 16, 51, 135, 74, 24, 53, 134, 77, 83, 138, 57, 28, 98, 40, 139,85, 30, 146, 44, 99, 141, 31, 89, 147, 72, 162, 46, 101, 149, 52, 47,76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136, 195, 79,59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142, 143, 91, 201,32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56, 166, 114, 155,80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117, 171, 198, 178,92, 202, 199, 63, 144, 173, 121, 104, 179, 203, 94, 152, 210, 181, 108,95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111, 213, 118, 172,227, 159, 217, 119, 174, 122, 200, 180, 229, 175, 123, 64, 233, 204,182, 125, 206, 241, 183, 212, 96, 186, 207, 187, 214, 228, 112, 215,189, 218, 160, 120, 230, 219), (231, 176, 124, 234, 221, 126, 235, 184,242, 188, 208, 237, 127, 243), (216, 245, 190), (220, 249, 191, 232),222, (236, 223), (238, 244, 239, 246, 128), (247, 250, 251, 192), (253,224), 240, 248, 252, 254, 255, 256].

(26) When N=256, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be:

[1, 2, L₁ ^((m=251)), 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=251))=(5,10, 3, 12, 8, 23, 4, 15, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43,65, 21, 45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28,48, 55, 79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102,108, 142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53,92, 68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121,153, 128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125,133, 167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213,159, 187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105,41, 70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164,99, 131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140,175, 109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166,196, 200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144,112, 151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165,172, 201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250,139, 177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240,242, 251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247, 253,249).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43, 65, 21,45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28, 48, 55,79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102, 108,142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53, 92,68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121, 153,128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125, 133,167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213, 159,187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105, 41,70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164, 99,131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140, 175,109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166, 196,200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144, 112,151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165, 172,201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250, 139,177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240, 242,251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247, 253, 249),254, 255, 256].

(27) When N=512, the sequence is a Q sequence, and the Q sequence mayinclude four subsequences whose element locations are changeable. Avalue of n ranges from 1 to 4. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=469)), L₃ ^((m=31)), L₄ ^((m=2)), 508,510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=469))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257,21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73,258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265,42, 145, 29, 70, 50, 75, 161, 43, 273, 193, 71, 45, 132, 82, 16, 289,51, 135, 74, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 98, 40, 385,139, 85, 30, 262, 146, 44, 99, 141, 31, 89, 263, 147, 72, 266, 162, 46,101, 149, 52, 47, 76, 267, 105, 274, 165, 194, 54, 163, 269, 78, 153,275, 55, 84, 58, 113, 86, 136, 290, 195, 79, 291, 59, 277, 169, 100,140, 197, 87, 177, 61, 90, 281, 102, 148, 293, 142, 322, 143, 91, 201,32, 103, 264, 106, 323, 150, 297, 48, 93, 209, 268, 386, 325, 305, 164,154, 151, 107, 56, 166, 387, 329, 270, 114, 155, 80, 225, 167, 276, 109,271, 60, 115, 196, 170, 157, 88, 62, 278, 292, 279, 117, 171, 198, 178,282, 92, 202, 389, 294, 199, 63, 144, 337, 173, 283, 121, 104, 179, 295,203, 94, 324, 393, 298, 152, 210, 285, 181, 108, 95, 205, 299, 353, 326,156, 110, 401, 306, 301, 211, 185, 327, 116, 168, 158, 226, 307, 330,111, 213, 118, 172, 331, 227, 388, 309, 159, 417, 338, 217, 272, 119,280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 175, 394, 284,123, 64, 341, 449, 354, 395, 233, 204, 296, 286, 182, 125, 206, 241,287, 300, 355, 183, 402, 212, 397, 345, 96, 186, 207, 328, 403, 187,357, 308, 419, 214, 302, 228, 303, 361, 112, 418, 215, 405, 310, 189,450, 332, 218, 160, 120, 230, 334, 409, 311, 421, 219, 369, 231, 392,176, 314, 340, 335, 124, 234, 315, 342, 451, 221, 425, 356, 126, 235,184, 396, 242, 317, 343, 346, 404, 288, 398, 453, 433, 188, 358, 208,237, 347, 362, 127, 243, 406, 216, 399, 304, 359, 420, 457, 349, 245,190, 220, 312, 363, 465, 407, 422, 249, 191, 370, 410, 411, 481, 232,316, 365, 423, 336, 371, 222, 452, 426, 413, 454, 318, 236, 344, 373,223, 427, 434, 238, 348, 244, 455, 319, 377, 429, 239, 360, 459, 400,435, 458, 246, 350, 128, 408, 437, 364, 466, 351, 247, 250, 461, 412,366, 441, 375, 424, 467, 251, 372, 192, 482, 414, 367, 469, 374, 428,415, 253, 483, 430, 224, 456, 473, 378, 436, 320, 485, 431, 489, 460,240, 379, 438, 462, 381, 248, 442, 352, 470, 439, 463, 252, 497, 468,368, 443, 475, 484, 380, 416, 254, 445, 486, 471, 376, 474, 432, 487,490, 255, 477); L₃ ^((m=31))=(440, 493, 382, 499, 464, 491, 383, 472,498, 444, 501, 446, 447, 476, 488, 478, 494, 505, 256, 492, 479, 384,500, 503, 495, 502, 448, 506, 507, 480, 509); and L₄ ^((m=2))=(504,496).

In this example, the Q sequence is specifically: [1, 43, 273, 193, 71,45, 132, 82, 16, 289, 51, 135, 74, 24, 53, 321, 134, 77, 83, 138, 57,28, 260, 98, 40, 385, 139, 85, 30, 262, 146, 44, 99, 141, 31, 89, 263,147, 72, 266, 162, 46, 101, 149, 52, 47, 76, 267, 105, 274, 165, 194,54, 163, 269, 78, 153, 275, 55, 84, 58, 113, 86, 136, 290, 195, 79, 291,59, 277, 169, 100, 140, 197, 87, 177, 61, 90, 281, 102, 148, 293, 142,322, 143, 91, 201, 32, 103, 264, 106, 323, 150, 297, 48, 93, 209, 268,386, 325, 305, 164, 154, 151, 107, 56, 166, 387, 329, 270, 114, 155, 80,225, 167, 276, 109, 271, 60, 115, 196, 170, 157, 88, 62, 278, 292, 279,117, 171, 198, 178, 282, 92, 202, 389, 294, 199, 63, 144, 337, 173, 121,104, 179, 295, 203, 94, 324, 393, 298, 152, 210, 285, 181, 108, 95, 205,299, 353, 326, 156, 110, 401, 306, 301, 211, 185, 327, 116, 168, 158,226, 307, 330, 111, 213, 118, 172, 331, 227, 388, 309, 159, 417, 338,217, 272, 119, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391,175, 394, 123, 64, 341, 449, 354, 395, 233, 204, 296, 286, 182, 125,206, 241, 287, 300, 355, 183, 402, 212, 397, 345, 96, 186, 207, 328,403, 187, 357, 308, 419, 214, 302, 228, 303, 361, 112, 418, 215, 405,310, 189, 450, 332, 218, 160, 120, 230, 334, 409, 311, 421, 219, 369,231, 392, 176, 314, 340, 335, 124, 234, 315, 342, 451, 221, 425, 356,126, 235, 184, 396, 242, 317, 343, 346, 404, 288, 398, 453, 433, 188,358, 208, 237, 347, 362, 127, 243, 406, 216, 399, 304, 359, 420, 457,349, 245, 190, 220, 312, 363, 465, 407, 422, 249, 191, 370, 410, 411,481, 232, 316, 365, 423, 336, 371, 222, 452, 426, 413, 454, 318, 236,344, 373, 223, 427, 434, 238, 348, 244, 455, 319, 377, 429, 239, 360,459, 400, 435, 458, 246, 350, 128, 408, 437, 364, 466, 351, 247, 250,461, 412, 366, 441, 375, 424, 467, 251, 372, 192, 482, 414, 367, 469,374, 428, 415, 253, 483, 430, 224, 456, 473, 378, 436, 320, 485, 431,489, 460, 240, 379, 438, 462, 381, 248, 442, 352, 470, 439, 463, 252,497, 468, 368, 443, 475, 484, 380, 416, 254, 445, 486, 471, 376, 474,432, 487, 490, 255, 477), (440, 493, 382, 499, 464, 491, 383, 472, 498,444, 501, 446, 447, 476, 488, 478, 494, 505, 256, 492, 479, 384, 500,503, 495, 502, 448, 506, 507, 480, 509), (504, 496), 508, 510, 511,512].

(28) When N=512, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=507)), 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=507))=(5,10, 3, 12, 8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38,46, 72, 22, 49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83,29, 53, 60, 90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164,79, 119, 127, 177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97,36, 71, 58, 105, 76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182,94, 136, 144, 192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147,203, 107, 149, 163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187,237, 248, 309, 202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65,31, 75, 70, 122, 44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139,102, 151, 162, 211, 115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112,160, 109, 165, 173, 230, 129, 180, 188, 238, 200, 252, 260, 319, 134,190, 204, 255, 214, 273, 280, 333, 227, 286, 290, 344, 304, 361, 369,424, 62, 110, 124, 179, 132, 189, 196, 254, 145, 193, 206, 270, 217,275, 287, 346, 155, 212, 226, 282, 236, 294, 301, 353, 246, 307, 315,362, 328, 380, 389, 435, 172, 232, 240, 296, 256, 310, 317, 269, 324,332, 386, 347, 392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450,368, 414, 422, 456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148,52, 98, 106, 156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186,249, 137, 191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140,195, 205, 271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233,292, 242, 303, 313, 363, 258, 320, 325, 336, 385, 396, 440, 74, 142,150, 208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378,199, 245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406,412, 452, 219, 267, 279, 330, 291, 345, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300, 293, 314, 367,377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403, 439,409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266, 305,327, 381, 342, 384, 395, 436, 404, 401, 444, 415, 448, 455, 480, 365,411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475, 491, 496,505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481, 495, 477,492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493, 503, 504,509, 506).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38, 46, 72, 22,49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83, 29, 53, 60,90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164, 79, 119, 127,177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97, 36, 71, 58, 105,76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182, 94, 136, 144,192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147, 203, 107, 149,163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187, 237, 248, 309,202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65, 31, 75, 70, 122,44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139, 102, 151, 162, 211,115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112, 160, 109, 165, 173,230, 129, 180, 188, 238, 200, 252, 260, 319, 134, 190, 204, 255, 214,273, 280, 333, 227, 286, 290, 344, 304, 361, 369, 424, 62, 110, 124,179, 132, 189, 196, 254, 145, 193, 206, 270, 217, 275, 287, 346, 155,212, 226, 282, 236, 294, 301, 353, 246, 307, 315, 362, 328, 380, 389,435, 172, 232, 240, 296, 256, 310, 317, 374, 269, 324, 332, 386, 347,392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450, 368, 414, 422,456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148, 52, 98, 106,156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186, 249, 137,191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140, 195, 205,271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233, 292, 242,303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440, 74, 142, 150,208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378, 199,245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406, 412,452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314,367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403,439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266,305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455,480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475,491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481,495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493,503, 504, 509, 506), 510, 511, 512].

(29) When N=1024, the sequence is a Q sequence, and the Q sequence mayinclude three (n=3) subsequences whose element locations are changeable.The sequence may be:

[1, 2, L₁ ^((m=3)), 17 L₂ ^((m=1012)), L₃ ^((m=2)), 1020, 1022, 1023,1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=1012))=(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18,11, 257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69,49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 517, 38,26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273, 193, 71,45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77, 83, 138,57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44, 99, 141,31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577, 76, 267,105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525, 84, 58,113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100, 140, 197,87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91, 201,546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209, 268, 386,325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387, 578, 329,549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196, 170,157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178, 282, 92,553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534, 401,306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307, 548,330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394, 284,773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395, 233,204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543, 335,124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621, 466,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374,575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795,865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722,320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240,818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 846, 921,472, 823, 852, 731, 498, 881, 444, 904, 688, 826, 501, 446, 933, 847,636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638, 908, 488, 696,747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800, 700, 494, 505,749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479, 384, 911, 816,918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923, 875, 977, 919,503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848, 993, 448, 734,828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830, 966, 939, 885,507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751, 872, 971, 912,758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863, 762, 509, 973,924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926, 879, 981,942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948, 832, 508,943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510, 864, 982,951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511, 766, 957,998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958,976, 512, 1003, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017,991, 1012, 768, 1004, 1015, 1007, 1018, 1014, 992, 1019, 960, 1021); andL₃ ^((m=2))=(1016, 1008).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66,8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131,27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145,29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51,135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40,385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519,266, 162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54,516, 163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518,195, 79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90,281, 102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106,530, 323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533,164, 154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225,167, 276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292,520, 279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199,524, 63, 144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94,324, 561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770,299, 353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327,539, 116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172,551, 331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550,119, 280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339,657, 313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64,341, 705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286,182, 125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397,345, 587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357,589, 569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650,772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552,651, 120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369,231, 653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659,613, 342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242,558, 661, 617, 317, 343, 779, 564, 404, 288, 398, 453, 675, 559, 786,433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 566, 362, 127, 243,590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457, 787, 245,570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803, 407, 681, 422,789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709, 481, 614, 232,573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612, 452, 602, 426,805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544, 373, 655, 223,615, 427, 776, 434, 560, 238, 899, 618, 809, 244, 721, 455, 666, 319,605, 377, 662, 429, 780, 239, 676, 360, 837, 459, 626, 400, 663, 678,435, 568, 458, 817, 246, 619, 350, 788, 128, 782, 898, 408, 667, 437,592, 364, 621, 466, 737, 351, 679, 572, 247, 682, 250, 627, 461, 708,841, 412, 783, 366, 790, 441, 600, 375, 669, 629, 424, 901, 467, 849,804, 251, 791, 372, 710, 192, 574, 690, 482, 683, 414, 604, 794, 367,714, 469, 711, 374, 575, 656, 428, 807, 415, 685, 905, 253, 616, 483,633, 806, 430, 795, 865, 224, 691, 456, 715, 836, 473, 810, 378, 606,620, 436, 664, 722, 320, 797, 485, 693, 913, 431, 607, 717, 489, 811,460, 839, 668, 240, 818, 622, 379, 838, 723, 438, 697, 462, 738, 680,381, 813, 628, 248, 900, 842, 442, 623, 929, 352, 725, 784, 470, 630,819, 439, 670, 463, 739, 684, 252, 843, 850, 497, 902, 821, 729, 468,634, 903, 368, 671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712,380, 866, 796, 416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486,808, 687, 907, 471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432,695, 812, 487, 753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477,698, 726, 915, 440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815,499, 873, 740, 930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730,701, 383, 742, 846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904,688, 826, 501, 446, 933, 847, 636, 746, 827, 733, 447, 963, 937, 476,854, 868, 638, 908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478,910, 720, 800, 700, 494, 505, 749, 945, 859, 874, 639, 755, 256, 969,870, 492, 479, 384, 911, 816, 918, 728, 871, 702, 932, 861, 500, 757,732, 824, 923, 875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922,877, 502, 848, 993, 448, 734, 828, 883, 935, 964, 506, 938, 748, 856,925, 735, 830, 966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831,889, 941, 751, 872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640,759, 949, 863, 762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504,884, 704, 994, 926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940,985, 968, 890, 948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893,972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987,996, 892, 928, 511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767,989, 952, 1005, 894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956,988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007,1018, 896, 1014, 992, 1019, 960, 1021), (1016, 1008), 1020, 1022, 1023,1024].

(30) When N=1024, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=1019)), 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁^((m=1019))=(5, 11, 3, 13, 8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18,14, 31, 21, 40, 48, 77, 23, 52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43,26, 51, 47, 89, 30, 56, 63, 97, 68, 108, 112, 170, 36, 60, 73, 111, 78,120, 127, 185, 84, 130, 139, 201, 149, 208, 226, 323, 9, 24, 27, 54, 35,59, 67, 104, 38, 75, 61, 114, 81, 124, 137, 194, 44, 70, 82, 129, 92,132, 146, 206, 101, 150, 159, 219, 172, 239, 251, 356, 53, 88, 98, 143,109, 152, 163, 234, 116, 165, 184, 250, 198, 259, 277, 378, 131, 192,202, 269, 213, 280, 296, 395, 232, 303, 319, 416, 339, 431, 464, 574,15, 28, 41, 69, 32, 80, 74, 133, 46, 83, 91, 144, 99, 156, 158, 227, 57,95, 103, 153, 110, 168, 183, 244, 125, 182, 193, 258, 205, 272, 288,390, 62, 107, 122, 181, 118, 186, 196, 270, 141, 204, 214, 281, 230,301, 314, 411, 147, 217, 235, 306, 248, 338, 348, 433, 266, 357, 364,452, 386, 482, 498, 613, 66, 119, 136, 203, 145, 215, 224, 304, 160,221, 238, 332, 252, 340, 358, 454, 173, 246, 265, 350, 279, 371, 383,468, 293, 389, 406, 484, 426, 518, 536, 641, 195, 273, 284, 373, 307,396, 408, 508, 331, 419, 432, 530, 460, 542, 557, 667, 341, 435, 465,547, 480, 570, 588, 681, 496, 590, 609, 698, 633, 727, 757, 844, 20, 39,45, 86, 49, 94, 102, 164, 55, 106, 115, 174, 123, 191, 200, 294, 65,117, 126, 197, 140, 209, 212, 297, 151, 218, 231, 317, 247, 337, 345,445, 72, 134, 138, 210, 154, 223, 236, 336, 169, 243, 254, 346, 263,372, 374, 471, 177, 262, 274, 368, 287, 385, 403, 486, 311, 412, 420,510, 439, 528, 551, 654, 79, 157, 167, 240, 176, 256, 267, 359, 189,276, 283, 388, 299, 397, 415, 514, 228, 291, 309, 413, 324, 423, 440,532, 352, 441, 461, 545, 479, 572, 585, 687, 255, 328, 347, 428, 365,453, 473, 559, 377, 463, 488, 581, 512, 597, 621, 708, 407, 500, 516,611, 534, 625, 601, 740, 553, 648, 670, 720, 678, 772, 791, 849, 90,175, 187, 286, 222, 300, 313, 410, 242, 316, 330, 434, 351, 446, 469,563, 261, 349, 362, 444, 384, 467, 492, 577, 398, 502, 504, 595, 524,618, 630, 723, 290, 381, 370, 475, 404, 494, 513, 604, 427, 522, 538,628, 555, 638, 659, 747, 451, 540, 566, 651, 579, 673, 693, 765, 599,684, 711, 802, 730, 807, 814, 878, 326, 387, 425, 520, 447, 526, 549,643, 477, 568, 561, 664, 592, 675, 695, 783, 490, 583, 606, 705, 623,690, 737, 795, 646, 743, 714, 817, 761, 831, 848, 899, 506, 616, 635,717, 656, 733, 750, 822, 662, 754, 787, 847, 769, 836, 871, 938, 701,799, 776, 858, 806, 875, 866, 929, 837, 884, 894, 949, 920, 961, 975,993, 10, 33, 76, 121, 50, 135, 105, 211, 64, 155, 171, 225, 128, 249,257, 333, 87, 166, 142, 237, 180, 260, 292, 361, 178, 298, 268, 382,312, 399, 414, 533, 96, 161, 207, 275, 190, 295, 282, 393, 220, 308,321, 417, 335, 436, 449, 541, 241, 327, 344, 443, 355, 462, 470, 567,367, 481, 499, 587, 509, 614, 626, 738, 113, 188, 199, 302, 245, 315,334, 430, 229, 343, 353, 456, 366, 466, 483, 580, 271, 363, 376, 489,392, 472, 497, 600, 405, 521, 531, 619, 552, 649, 660, 759, 289, 391,401, 519, 422, 507, 537, 634, 438, 544, 571, 650, 582, 669, 685, 774,476, 562, 591, 680, 603, 691, 713, 788, 636, 706, 729, 810, 745, 820,842, 915, 148, 216, 264, 342, 233, 360, 369, 485, 285, 379, 394, 501,409, 525, 535, 627, 310, 402, 421, 511, 437, 554, 564, 652, 455, 550,578, 666, 602, 694, 709, 780, 320, 429, 448, 558, 459, 565, 586, 677,493, 589, 617, 697, 631, 715, 735, 804, 515, 615, 642, 718, 657, 731,748, 823, 674, 762, 771, 835, 790, 855, 872, 931, 325, 458, 487, 593,505, 612, 624, 719, 529, 622, 644, 739, 661, 758, 770, 833, 548, 653,672, 752, 688, 763, 784, 853, 704, 789, 798, 860, 813, 879, 889, 942,584, 676, 696, 778, 726, 792, 801, 868, 732, 811, 824, 886, 838, 895,904, 951, 751, 826, 843, 898, 859, 908, 916, 956, 869, 919, 928, 966,937, 976, 985, 1008, 179, 253, 278, 380, 318, 400, 418, 539, 305, 424,442, 556, 457, 575, 596, 689, 322, 450, 478, 573, 495, 598, 610, 710,517, 620, 639, 722, 655, 746, 753, 834, 329, 474, 491, 608, 523, 637,629, 734, 546, 647, 663, 749, 679, 773, 775, 851, 569, 668, 692, 703,782, 796, 861, 724, 805, 812, 880, 825, 890, 901, 948, 354, 527, 503,645, 560, 671, 665, 594, 683, 699, 786, 712, 793, 809, 876, 607, 700,716, 797, 744, 818, 827, 887, 755, 828, 840, 897, 857, 911, 918, 962,640, 721, 741, 819, 768, 846, 854, 905, 777, 841, 863, 913, 874, 923,934, 969, 800, 870, 881, 930, 893, 940, 925, 980, 902, 946, 954, 973,957, 989, 995, 1013, 375, 576, 543, 682, 605, 702, 707, 803, 632, 728,736, 821, 756, 832, 850, 907, 658, 742, 764, 829, 781, 852, 865, 914,794, 873, 862, 922, 888, 933, 939, 974, 686, 779, 760, 856, 808, 867,882, 926, 816, 885, 892, 943, 903, 936, 950, 982, 839, 896, 909, 947,917, 955, 964, 987, 924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785,815, 883, 830, 891, 900, 945, 845, 910, 906, 958, 921, 952, 965, 992,864, 912, 927, 968, 935, 963, 979, 996, 944, 981, 971, 999, 986, 1004,1006, 1015, 877, 932, 941, 972, 953, 978, 983, 1002, 959, 984, 994,1009, 988, 1003, 1011, 1020, 967, 997, 990, 1007, 1000, 1014, 1010,1019, 1005, 1012, 1016, 1021, 1018).

In this example, the Z sequence is specifically: [1, 2, (5, 11, 3, 13,8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40, 48, 77, 23,52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89, 30, 56, 63,97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185, 84, 130, 139,201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104, 38, 75, 61,114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206, 101, 150,159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163, 234, 116,165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213, 280, 296,395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69, 32, 80, 74,133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153, 110, 168,183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107, 122, 181,118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411, 147, 217,235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482, 498, 613,66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332, 252, 340,358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389, 406, 484,426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508, 331, 419,432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570, 588, 681,496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49, 94, 102,164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197, 140, 209,212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134, 138, 210,154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471, 177, 262,274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528, 551, 654,79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388, 299, 397,415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441, 461, 545,479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559, 377, 463,488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625, 601, 740,553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286, 222, 300,313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349, 362, 444,384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723, 290, 381,370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638, 659, 747,451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802, 730, 807,814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568, 561, 664,592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795, 646, 743,714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733, 750, 822,662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858, 806, 875,866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76, 121, 50,135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166, 142, 237,180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533, 96, 161,207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436, 449, 541,241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587, 509, 614,626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343, 353, 456,366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600, 405, 521,531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507, 537, 634,438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680, 603, 691,713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216, 264, 342,233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627, 310, 402,421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694, 709, 780,320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697, 631, 715,735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762, 771, 835,790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719, 529, 622,644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763, 784, 853,704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778, 726, 792,801, 868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826, 843, 898,859, 908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008, 179, 253,278, 380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575, 596, 689,322, 450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722, 655, 746,753, 834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647, 663, 749,679, 773, 775, 851, 569, 668, 692, 766, 703, 782, 796, 861, 724, 805,812, 880, 825, 890, 901, 948, 354, 527, 503, 645, 560, 671, 665, 767,594, 683, 699, 786, 712, 793, 809, 876, 607, 700, 716, 797, 744, 818,827, 887, 755, 828, 840, 897, 857, 911, 918, 962, 640, 721, 741, 819,768, 846, 854, 905, 777, 841, 863, 913, 874, 923, 934, 969, 800, 870,881, 930, 893, 940, 925, 980, 902, 946, 954, 973, 957, 989, 995, 1013,375, 576, 543, 682, 605, 702, 707, 803, 632, 728, 736, 821, 756, 832,850, 907, 658, 742, 764, 829, 781, 852, 865, 914, 794, 873, 862, 922,888, 933, 939, 974, 686, 779, 760, 856, 808, 867, 882, 926, 816, 885,892, 943, 903, 936, 950, 982, 839, 896, 909, 947, 917, 955, 964, 987,924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785, 815, 883, 830, 891,900, 945, 845, 910, 906, 958, 921, 952, 965, 992, 864, 912, 927, 968,935, 963, 979, 996, 944, 981, 971, 999, 986, 1004, 1006, 1015, 877, 932,941, 972, 953, 978, 983, 1002, 959, 984, 994, 1009, 988, 1003, 1011,1020, 967, 997, 990, 1007, 1000, 1014, 1010, 1019, 1005, 1012, 1016,1021, 1018), 1022, 1023, 1024].

In the foregoing example sequences, locations of elements in thesubsequence L_(n) ^((m)) may be adjusted in the subsequence. Forexample, in an example (1) in Example 1, L₁ ^((m=3))=(5, 9, 3), and thenlocations of elements in a first subsequence L₁ ^((m=3)) in the sequencemay be adjusted to (5, 3, 9), (3, 5, 9), (3, 9, 5), (5, 9, 3), (9, 3,5), (9, 5, 3), or the like. A new sequence is obtained after theadjustment. In the foregoing specific sequences, an element set inparentheses represents the foregoing subsequence L_(n) ^((m)), andlocations of elements in the parentheses may be exchanged with eachother, but the locations of the elements in the parentheses cannot beexchanged with locations of elements outside the parentheses.

A process of performing polar coding based on a sequence in thisembodiment of this application is described below by using an example.

The sequence in this embodiment of this application meets a simplenesting characteristic, that is, another sequence with a relativelyshort mother code length may be obtained based on a sequence with arelatively long mother code length. Specifically, for example, asequence with a relatively short mother code length of N₂ is obtainedbased on a sequence with a relatively long mother code length of N₁.Elements whose sequence numbers are less than or equal to N₂ areextracted from the sequence with the relatively long mother code lengthof N₁, and an obtained subsequence is the sequence with the relativelyshort mother code length of N₂. An order of the elements in the obtainedsequence with the relatively short mother code length of N₂ is the sameas an order of these elements in the sequence with the relatively longmother code length of N₁. It is assumed that the to-be-coded bits with alength of K includes information bits with a length of K_(info) and acheck bit with a length of K_(CRC), a code length is M, and a mothercode length is N, where K=27, K_(info)=8, K_(CRC)=19, M=60, and N=64.When a parameter is constructed for a polar code, a sequence of N=64needs to be obtained. It is assumed that the obtained sequence is a Qsequence. The Q sequence in the foregoing example sequences of N=64 maybe directly used in this embodiment of this application, or the Qsequence of N=64 may be obtained based on the nesting characteristicfrom Q sequences of N>64. For example, the Q sequence of N=128 inExample 1 is used. All sequence numbers whose subchannel sequencenumbers are less than or equal to 64 are extracted, and an order of theobtained sequence numbers remains unchanged to form a new sequence ofN=64: [1, 2, (5, 9, 3), 17, 33, (7, 4, 13, 6, 19, 10, 34, 18, 11), 21,35, 25, (8, 37), (12, 41), (20, 14, 49), 15, 22, (27, 36, 39, 23, 38,26), 42, 29, (50, 43, 45, 16, 51, 24, 53), (57, 28, 40), 30, (44, 31,46), 52, 47, 54, (55, 58), 59, 61, 32, 48, 56, 62, 63, 64]. Locations ofelements in some subsequences in the sequence may be exchanged.Therefore, the new sequence of N=64 obtained based on the nestingcharacteristic from the sequence of N=128 is slightly different from thesequence of N=64 in the example (1) in Example 1: A range of parenthesesis larger, and more sequences can be formed.

For example, the Q sequence of N=64 in the example (1) in Example 1 isdirectly obtained. Locations of K polarized channels are selected indescending order of reliability based on the obtained Q sequence, toplace the to-be-coded bits, where K=27. To be specific, the to-be-codedbits are placed at locations of polarized channels whose sequencenumbers are (43, 45, 16, 51, 24, 53, 57, 28, 40, 30, 44, 31, 46, 52, 47,54, 55, 58, 59, 61, 32, 48, 56, 60, 62, 63, 64) or at locations ofpolarized channels whose sequence numbers are (50, 45, 16, 51, 24, 53,57, 28, 40, 30, 44, 31, 46, 52, 47, 54, 55, 58, 59, 0, 32, 48, 56, 60,62, 63, 64). In the directly obtained Q sequence of N=64, locations oftwo elements (50, 43) in the subsequence L₁ ^((m=3))=(50, 43) may bemutually exchanged. Therefore, there may be two possible combinations.The to-be-coded bits are placed, with equal positions, in polarizedchannels corresponding to the subsequences L₁ ^((m=3))=(16.5); L₂^((m=2))=(24.53); L₁₀ ^((m=2))=(57.28); L₁₅ ^((m=2))=(44.31). Therefore,whether to exchange elements does not need to be considered.

A prerequisite for the foregoing example of placing the information bitsis that sending priorities of the 27 to-be-coded bits are the same. Ifthe priorities of the to-be-coded bits are different, for example, 18check bits need to be placed at locations of 18 polarized channels withhighest reliability in the selected 27 polarized channels, and one checkbit needs to be placed at a location whose reliability is lower thanthat of some information bits. In this case, when the check bit isplaced, orders of the check bit in the four subsequences L₁ ^((m=2)) toL₁₀ ^((m=2)) may be considered. For example, the check bit needs to beplaced at a first location in L₁ ^((m=2)). When L₂ ^((m=2))=(16.51), thefirst location is 16, and after orders of 16 and 51 are exchanged, thefirst location is 51. Therefore, whether a location of 16 or a locationof 51 is selected for the check bit may affect final performance.

Locations other than locations at which the to-be-coded bits are placedare locations of frozen bits. Polar coding and rate matching areperformed based on the locations of the to-be-coded bits and thelocations of the frozen bits.

In addition, a new sequence of N=64 may be obtained based on the nestingcharacteristic by using the following sequences: a sequence of N=256, asequence of N=512, or a sequence of N=1024.

An example of N=64 is used for description above, and a coding method ofanother code length is similar to this. Details are not described hereinagain.

The sequences (1) to (30) in the foregoing examples in this embodimentof this application may be obtained by taking an intersection set ofseveral groups of sequences. For example, the sequence (1) in theforegoing example is obtained by taking an intersection set of severalgroups of sequences whose mother code lengths are 64. Certainly, thesequence may be obtained in another manner.

In a possible example, the following sequences S1 to S20 are obtainedthrough simulation. The sequences S1 to S20 are sequences whose mothercode lengths are 1024. Based on the nesting characteristic, sequenceswhose mother code lengths are 64, 128, 256, and 512 may be separatelyobtained based on the sequences S1 to S20, to obtain 20 groups ofsequences whose mother code lengths are separately 64, 128, 256, 512,and 1024. Sequences in examples (1) to (10) in Example 1 may be obtainedbased on a first group of sequences to a fifth group of sequences.Sequences in examples (11) to (20) in Example 2 may be obtained based onthe first group of sequences to a tenth group of sequences. Sequences inexamples (21) to (30) in Example 3 may be obtained based on the firstgroup of sequences to a twentieth group of sequences. It may beunderstood that a larger quantity of combined sequences indicates asmaller quantity of elements whose locations remain unchanged in anobtained sequence, a larger quantity of elements whose locations arechangeable, and a larger range of the obtained sequence.

In this embodiment of this application, the polar coding method shown inFIG. 2 may further be performed by using any one of the sequences S1 toS20.

Specifically, the sequences S1 to S20 may be as follows:

sequence S1: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 18, 129, 13,19, 34, 21, 35, 25, 257, 37, 66, 8, 67, 41, 12, 69, 130, 14, 49, 20,131, 513, 73, 15, 22, 36, 133, 81, 23, 26, 258, 38, 137, 97, 27, 259,39, 68, 42, 145, 29, 261, 70, 43, 50, 71, 161, 132, 265, 514, 45, 74,16, 51, 134, 515, 75, 273, 53, 82, 24, 193, 135, 517, 77, 83, 138, 57,289, 98, 28, 260, 40, 85, 139, 521, 146, 30, 99, 262, 44, 141, 147, 529,89, 321, 101, 31, 263, 72, 162, 266, 46, 52, 149, 163, 545, 105, 267,516, 47, 76, 274, 54, 153, 385, 165, 194, 136, 269, 518, 78, 113, 275,55, 84, 58, 290, 195, 577, 519, 79, 169, 277, 86, 140, 522, 59, 291,100, 197, 87, 142, 523, 177, 148, 281, 530, 61, 90, 293, 322, 102, 32,264, 641, 201, 143, 525, 150, 531, 91, 323, 103, 164, 297, 546, 106,268, 48, 209, 151, 533, 93, 325, 154, 386, 166, 547, 107, 270, 305, 114,276, 56, 225, 155, 537, 387, 769, 167, 549, 196, 329, 578, 109, 271,520, 80, 115, 170, 278, 60, 292, 157, 389, 198, 579, 337, 117, 171, 279,553, 88, 524, 178, 282, 62, 294, 199, 581, 393, 642, 173, 202, 144, 526,179, 561, 121, 353, 283, 532, 63, 92, 295, 324, 104, 298, 643, 203, 585,401, 527, 181, 210, 152, 285, 534, 94, 326, 299, 548, 108, 645, 306,205, 211, 593, 535, 95, 327, 185, 417, 226, 156, 538, 388, 770, 168,301, 550, 330, 110, 272, 307, 116, 213, 649, 158, 227, 609, 539, 390,771, 551, 331, 580, 111, 309, 338, 118, 172, 280, 554, 657, 217, 449,229, 159, 541, 391, 773, 200, 333, 582, 339, 119, 394, 174, 555, 180,313, 562, 122, 354, 284, 64, 296, 583, 673, 233, 341, 395, 644, 777,175, 557, 204, 586, 402, 528, 182, 563, 123, 286, 355, 300, 397, 646,206, 587, 241, 403, 785, 183, 565, 212, 345, 594, 125, 357, 287, 536,96, 328, 186, 418, 302, 705, 647, 308, 207, 589, 405, 214, 595, 650,187, 569, 419, 801, 228, 361, 610, 540, 772, 303, 552, 332, 112, 310,215, 597, 651, 409, 658, 189, 218, 421, 450, 230, 160, 542, 611, 392,774, 334, 369, 311, 340, 120, 556, 653, 659, 219, 601, 451, 833, 231,613, 543, 775, 335, 584, 425, 674, 234, 342, 396, 778, 176, 558, 564,124, 661, 356, 221, 453, 675, 235, 343, 617, 398, 779, 433, 559, 588,242, 404, 786, 184, 317, 566, 346, 126, 358, 288, 665, 897, 677, 457,706, 237, 399, 648, 781, 208, 590, 243, 625, 406, 787, 567, 347, 596,127, 359, 188, 570, 420, 802, 362, 304, 707, 465, 591, 245, 407, 681,789, 216, 349, 598, 652, 410, 190, 571, 422, 803, 363, 612, 709, 370,312, 599, 654, 689, 249, 481, 411, 660, 793, 191, 573, 220, 423, 602,805, 452, 834, 232, 365, 614, 544, 776, 336, 371, 426, 713, 655, 316,413, 662, 222, 603, 454, 835, 615, 373, 427, 676, 809, 236, 344, 618,780, 434, 560, 318, 721, 663, 223, 605, 455, 837, 666, 898, 429, 678,458, 238, 619, 400, 782, 435, 817, 244, 377, 626, 788, 319, 568, 348,128, 360, 737, 667, 899, 679, 459, 708, 841, 239, 621, 783, 437, 466,592, 246, 627, 408, 682, 790, 350, 572, 804, 669, 364, 901, 461, 710,467, 849, 247, 629, 683, 791, 351, 600, 441, 690, 250, 482, 412, 794,192, 574, 424, 806, 366, 711, 372, 469, 905, 685, 714, 656, 691, 251,633, 414, 483, 865, 795, 575, 604, 807, 836, 367, 616, 374, 428, 810,715, 913, 693, 473, 722, 253, 485, 415, 664, 797, 224, 606, 456, 838,375, 430, 811, 620, 436, 818, 717, 378, 320, 723, 607, 839, 697, 929,489, 738, 668, 900, 431, 680, 813, 460, 842, 240, 622, 784, 438, 819,379, 628, 725, 670, 739, 902, 462, 843, 497, 623, 439, 821, 468, 850,248, 381, 630, 684, 792, 352, 442, 729, 961, 741, 671, 903, 463, 712,845, 470, 851, 631, 906, 686, 443, 692, 825, 252, 634, 484, 866, 796,576, 808, 368, 471, 745, 853, 907, 687, 716, 914, 445, 694, 474, 254,635, 486, 416, 798, 867, 376, 812, 909, 718, 753, 915, 695, 475, 724,857, 255, 637, 487, 869, 799, 608, 840, 698, 930, 490, 432, 814, 820,719, 380, 917, 477, 726, 699, 931, 491, 740, 873, 815, 844, 498, 624,440, 822, 382, 727, 921, 701, 730, 933, 962, 493, 742, 672, 904, 464,846, 499, 881, 823, 852, 383, 632, 444, 826, 731, 963, 743, 847, 501,937, 472, 746, 854, 908, 688, 446, 827, 636, 868, 733, 965, 747, 855,910, 945, 505, 754, 916, 447, 696, 829, 476, 858, 256, 638, 488, 870,800, 969, 749, 911, 720, 755, 918, 478, 859, 639, 871, 700, 932, 492,874, 816, 977, 757, 919, 479, 728, 861, 922, 702, 934, 494, 875, 500,882, 824, 384, 761, 993, 923, 703, 732, 935, 964, 495, 744, 877, 848,502, 883, 938, 828, 925, 734, 966, 503, 885, 939, 748, 856, 946, 506,448, 830, 735, 967, 941, 970, 750, 912, 947, 507, 756, 889, 831, 860,640, 872, 971, 751, 949, 978, 509, 758, 920, 480, 862, 876, 973, 979,759, 863, 953, 762, 994, 924, 704, 936, 496, 878, 884, 981, 763, 926,995, 879, 504, 886, 940, 985, 765, 997, 927, 736, 968, 887, 942, 948,508, 890, 832, 1001, 943, 972, 752, 950, 510, 891, 974, 1009, 951, 980,511, 760, 893, 864, 954, 975, 982, 955, 764, 996, 880, 983, 957, 986,766, 998, 928, 888, 987, 767, 999, 1002, 944, 892, 989, 1003, 1010, 952,512, 894, 1005, 976, 1011, 895, 956, 1013, 984, 958, 1017, 959, 988,768, 1000, 990, 1004, 991, 1006, 1012, 896, 1007, 1014, 1015, 1018, 960,1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S2: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 12, 130, 41, 69, 14, 20,131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261, 97,145, 27, 514, 39, 515, 265, 68, 42, 29, 161, 70, 43, 517, 50, 75, 273,193, 521, 529, 71, 45, 132, 16, 74, 289, 545, 51, 24, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 30, 85, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 72, 266, 46, 101, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 163, 274, 523, 641, 105, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 195, 290, 79, 169,277, 59, 86, 61, 87, 140, 100, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 106, 322, 293, 201, 323,578, 150, 297, 48, 93, 209, 549, 579, 268, 386, 325, 305, 164, 151, 107,56, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155, 276,60, 271, 115, 167, 524, 581, 561, 157, 196, 170, 198, 171, 278, 292,279, 117, 88, 62, 178, 282, 526, 643, 532, 527, 63, 92, 585, 770, 144,389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534, 645,535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210, 538,95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110, 156,327, 116, 111, 773, 550, 657, 539, 551, 168, 307, 330, 158, 226, 118,172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119, 541,554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 123, 394,284, 64, 175, 341, 449, 354, 395, 233, 204, 673, 555, 557, 562, 582,296, 286, 182, 206, 125, 785, 705, 183, 287, 528, 583, 644, 586, 563,300, 355, 212, 402, 186, 397, 345, 207, 302, 801, 96, 187, 241, 536,587, 565, 646, 594, 328, 403, 357, 308, 303, 833, 589, 647, 112, 540,569, 595, 650, 772, 228, 418, 332, 215, 405, 310, 189, 552, 610, 897,160, 218, 361, 419, 409, 369, 230, 450, 421, 542, 597, 651, 774, 658,311, 120, 334, 219, 543, 611, 176, 392, 231, 314, 124, 340, 335, 221,451, 425, 315, 556, 601, 653, 234, 775, 659, 613, 235, 288, 453, 126,342, 396, 778, 584, 558, 674, 356, 343, 564, 661, 559, 617, 779, 675,184, 398, 433, 317, 346, 242, 208, 404, 358, 786, 188, 588, 566, 665,625, 781, 237, 127, 243, 347, 399, 706, 216, 677, 787, 590, 567, 648,406, 359, 304, 570, 596, 362, 707, 190, 457, 349, 465, 802, 420, 407,245, 410, 591, 681, 789, 571, 598, 363, 573, 220, 422, 599, 652, 612,709, 602, 803, 370, 793, 312, 191, 654, 689, 603, 411, 232, 249, 365,336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 481, 236, 223,344, 318, 544, 373, 615, 427, 776, 128, 454, 238, 560, 834, 805, 713,835, 662, 809, 605, 618, 721, 780, 434, 898, 319, 455, 837, 817, 676,663, 348, 429, 400, 377, 244, 239, 458, 435, 360, 568, 619, 666, 737,899, 841, 782, 626, 350, 246, 459, 592, 678, 621, 667, 788, 572, 783,627, 679, 408, 364, 351, 437, 192, 247, 466, 412, 461, 250, 366, 600,708, 574, 669, 682, 790, 804, 791, 683, 629, 441, 690, 794, 604, 575,467, 424, 372, 251, 414, 367, 469, 482, 374, 656, 901, 806, 428, 415,253, 616, 849, 685, 795, 714, 633, 691, 807, 606, 483, 473, 224, 664,836, 905, 810, 715, 620, 797, 693, 375, 485, 430, 456, 722, 607, 717,811, 865, 838, 697, 723, 913, 818, 378, 436, 813, 320, 622, 240, 431,460, 379, 668, 839, 489, 438, 628, 623, 462, 381, 439, 352, 497, 680,725, 819, 842, 670, 738, 630, 468, 248, 442, 463, 470, 443, 252, 684,843, 739, 900, 821, 729, 929, 850, 671, 784, 631, 792, 845, 902, 686,368, 634, 712, 254, 692, 741, 851, 825, 903, 687, 471, 416, 484, 445,376, 474, 906, 796, 486, 635, 745, 853, 961, 866, 907, 716, 694, 808,475, 798, 637, 695, 255, 718, 576, 799, 812, 867, 432, 380, 698, 914,487, 724, 909, 857, 719, 477, 814, 608, 490, 699, 753, 840, 915, 726,869, 820, 815, 440, 491, 624, 382, 498, 493, 464, 672, 930, 844, 740,917, 822, 727, 632, 701, 873, 931, 921, 881, 730, 383, 499, 444, 446,472, 962, 933, 823, 742, 846, 731, 447, 688, 904, 636, 826, 743, 852,847, 256, 476, 733, 963, 937, 827, 746, 501, 488, 638, 505, 800, 696,854, 908, 868, 855, 747, 910, 829, 965, 858, 754, 720, 916, 870, 478,700, 749, 639, 816, 945, 755, 859, 911, 492, 479, 728, 918, 871, 384,494, 500, 874, 702, 969, 495, 861, 502, 932, 919, 757, 922, 875, 732,977, 934, 882, 761, 824, 703, 923, 744, 877, 848, 935, 828, 734, 883,448, 938, 503, 964, 925, 993, 748, 735, 856, 885, 939, 506, 966, 507,830, 750, 946, 860, 831, 967, 756, 941, 912, 872, 751, 889, 480, 970,947, 862, 758, 971, 509, 920, 640, 876, 863, 759, 949, 978, 924, 973,762, 878, 979, 496, 936, 704, 884, 953, 763, 504, 926, 879, 981, 994,886, 940, 927, 765, 736, 887, 995, 942, 968, 985, 508, 890, 948, 832,752, 943, 997, 972, 891, 1001, 510, 950, 974, 893, 951, 864, 760, 1009,511, 980, 954, 764, 975, 955, 880, 982, 983, 928, 996, 766, 957, 888,986, 998, 987, 944, 892, 999, 767, 512, 989, 1002, 952, 1003, 894, 976,895, 1010, 956, 1005, 1011, 958, 984, 959, 988, 1013, 1000, 1017, 768,990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960, 1015, 1018, 1019, 992,1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S3: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 8, 130, 67, 513, 12, 41, 69, 20, 14,131, 49, 15, 73, 258, 22, 133, 36, 23, 259, 81, 26, 137, 38, 27, 514,97, 261, 39, 515, 265, 68, 42, 145, 29, 70, 43, 517, 50, 161, 273, 71,289, 545, 45, 193, 521, 529, 132, 74, 51, 134, 82, 75, 16, 24, 53, 321,135, 77, 57, 83, 28, 138, 98, 40, 385, 260, 85, 139, 262, 30, 146, 44,99, 516, 89, 141, 31, 147, 46, 263, 72, 266, 101, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 105, 274, 523, 641, 163, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 79, 277, 195, 290,59, 169, 86, 140, 100, 87, 197, 142, 291, 61, 281, 546, 769, 90, 102,148, 177, 91, 143, 533, 547, 537, 293, 201, 264, 32, 150, 322, 323, 578,103, 106, 93, 48, 297, 164, 151, 209, 549, 579, 386, 268, 305, 325, 107,154, 387, 166, 56, 329, 114, 520, 553, 642, 155, 80, 109, 225, 270, 167,524, 581, 561, 60, 276, 271, 115, 196, 170, 292, 278, 157, 88, 171, 117,279, 198, 62, 282, 526, 643, 532, 527, 178, 294, 389, 92, 585, 770, 199,144, 63, 121, 202, 283, 173, 104, 337, 179, 295, 94, 534, 645, 535, 593,548, 771, 298, 393, 324, 285, 203, 181, 108, 152, 210, 538, 95, 205,299, 401, 326, 353, 649, 609, 306, 301, 156, 211, 110, 168, 185, 116,226, 327, 158, 111, 773, 550, 657, 539, 551, 307, 213, 330, 118, 172,331, 227, 388, 309, 272, 580, 417, 217, 338, 159, 777, 119, 541, 554,280, 333, 390, 174, 122, 200, 180, 229, 394, 284, 391, 175, 313, 123,673, 555, 557, 562, 582, 354, 204, 64, 182, 339, 296, 449, 341, 286,395, 233, 125, 785, 705, 206, 183, 287, 528, 583, 644, 586, 563, 300,355, 212, 402, 186, 397, 241, 536, 587, 565, 646, 594, 207, 302, 801,345, 403, 328, 357, 308, 96, 418, 214, 187, 405, 112, 540, 569, 595,650, 772, 303, 833, 589, 647, 228, 361, 215, 189, 552, 610, 897, 332,310, 419, 409, 218, 450, 230, 160, 421, 542, 597, 651, 774, 658, 392,334, 311, 369, 340, 120, 314, 219, 543, 611, 335, 231, 234, 775, 659,613, 176, 124, 315, 556, 601, 653, 342, 221, 425, 451, 396, 778, 584,558, 674, 356, 288, 184, 235, 126, 343, 564, 661, 559, 617, 779, 675,317, 242, 346, 453, 398, 404, 208, 433, 358, 786, 188, 588, 566, 665,625, 781, 237, 127, 243, 399, 706, 347, 457, 359, 406, 304, 570, 596,190, 216, 677, 787, 590, 567, 648, 362, 707, 245, 349, 420, 407, 465,802, 410, 591, 681, 789, 571, 598, 312, 363, 573, 220, 422, 599, 652,612, 709, 602, 803, 370, 793, 191, 654, 689, 603, 249, 232, 411, 336,365, 423, 614, 660, 655, 316, 222, 371, 426, 236, 452, 481, 413, 344,223, 318, 544, 373, 615, 427, 776, 454, 238, 560, 834, 805, 713, 835,662, 809, 605, 618, 721, 780, 348, 319, 244, 434, 898, 455, 837, 817,676, 663, 360, 568, 619, 666, 737, 899, 841, 782, 626, 429, 377, 400,239, 458, 435, 128, 350, 246, 459, 592, 678, 621, 667, 788, 572, 783,627, 679, 437, 408, 466, 364, 247, 351, 412, 461, 250, 366, 600, 708,574, 669, 682, 790, 804, 791, 710, 683, 629, 467, 192, 441, 690, 794,604, 575, 372, 424, 251, 482, 469, 367, 414, 374, 656, 901, 806, 711,428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606, 483, 473,224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 430, 456, 722, 607,717, 811, 865, 838, 697, 723, 913, 818, 378, 436, 813, 485, 320, 622,431, 240, 379, 668, 839, 460, 438, 628, 623, 489, 381, 462, 497, 680,725, 819, 842, 670, 738, 630, 352, 439, 468, 248, 442, 463, 470, 443,252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631, 792, 845,902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903, 687, 471, 416,484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866, 907, 716,694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812, 867, 432, 380,698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490, 699, 753, 840,915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493, 464, 672, 930,844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730, 383, 499,444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904, 636, 826,743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501, 488, 638, 505,800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720, 916, 870,478, 700, 749, 639, 816, 965, 945, 755, 859, 911, 492, 479, 728, 918,871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932, 919, 757, 922,875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877, 848, 935, 828,734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856, 885, 939, 506,966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872, 751, 889,480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759, 949, 978,924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504, 926, 879,981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985, 508, 890,948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974, 893, 951, 864,760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983, 928, 996, 766,957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989, 1002, 952, 1003,894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988, 1013, 1000,1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960, 1015, 1018,1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S4: [1, 2, 3, 5, 9, 17, 33, 4, 6, 513, 65, 7, 10, 11, 129, 18,13, 19, 34, 257, 21, 35, 25, 66, 37, 8, 130, 67, 12, 41, 69, 20, 514,14, 131, 49, 15, 73, 258, 22, 133, 36, 23, 259, 81, 26, 137, 38, 27,515, 97, 261, 39, 265, 68, 42, 145, 29, 70, 43, 50, 161, 273, 517, 71,289, 45, 193, 132, 74, 51, 134, 82, 75, 16, 521, 24, 53, 321, 135, 77,57, 83, 28, 138, 98, 529, 40, 385, 260, 85, 139, 262, 30, 146, 545, 44,99, 89, 141, 31, 147, 46, 263, 516, 72, 266, 101, 162, 52, 149, 47, 518,76, 267, 105, 274, 163, 54, 153, 577, 78, 269, 194, 165, 275, 55, 519,84, 136, 58, 113, 79, 277, 522, 195, 290, 59, 169, 86, 140, 523, 100,87, 197, 142, 291, 641, 61, 281, 90, 102, 148, 177, 530, 91, 143, 293,201, 264, 525, 32, 150, 322, 323, 531, 103, 106, 93, 48, 297, 546, 164,151, 209, 386, 769, 268, 305, 325, 107, 533, 154, 387, 166, 56, 329,547, 114, 155, 80, 537, 109, 225, 270, 167, 578, 60, 276, 271, 115, 549,196, 170, 292, 278, 520, 157, 88, 171, 642, 117, 279, 198, 62, 579, 282,178, 294, 524, 389, 92, 199, 144, 553, 63, 121, 202, 581, 283, 173, 104,532, 337, 179, 295, 526, 94, 298, 393, 643, 324, 285, 203, 561, 181,108, 152, 527, 210, 95, 205, 585, 299, 401, 326, 770, 353, 306, 534,301, 156, 211, 645, 110, 168, 185, 548, 116, 226, 535, 327, 158, 111,771, 307, 213, 593, 330, 118, 172, 538, 331, 227, 649, 388, 309, 272,550, 417, 217, 539, 338, 159, 609, 119, 280, 773, 333, 390, 174, 551,122, 200, 777, 180, 229, 580, 394, 284, 554, 391, 175, 657, 313, 123,541, 354, 204, 64, 582, 182, 339, 555, 296, 449, 562, 341, 286, 673,395, 785, 233, 125, 583, 206, 183, 801, 287, 300, 557, 355, 212, 705,402, 644, 397, 241, 586, 207, 302, 563, 345, 646, 403, 328, 594, 357,308, 587, 96, 528, 418, 214, 536, 405, 565, 112, 833, 303, 228, 647,361, 215, 589, 189, 569, 332, 310, 595, 419, 409, 540, 218, 650, 450,230, 610, 160, 552, 421, 392, 897, 334, 772, 311, 369, 597, 340, 651,120, 774, 314, 219, 542, 335, 658, 231, 234, 556, 176, 611, 124, 315,601, 342, 653, 221, 543, 425, 451, 659, 396, 558, 356, 775, 288, 584,184, 235, 778, 126, 613, 343, 674, 317, 242, 564, 346, 661, 453, 559,398, 588, 404, 208, 779, 433, 617, 358, 786, 188, 675, 237, 566, 127,665, 243, 399, 590, 347, 781, 457, 706, 359, 677, 406, 787, 304, 567,190, 596, 216, 648, 362, 570, 245, 349, 625, 420, 591, 407, 789, 465,707, 410, 802, 312, 571, 363, 681, 220, 598, 422, 652, 370, 612, 191,599, 249, 709, 232, 654, 411, 803, 336, 573, 365, 793, 423, 316, 222,602, 371, 614, 426, 660, 236, 689, 452, 603, 481, 655, 413, 805, 344,713, 223, 776, 318, 544, 373, 662, 427, 834, 454, 835, 238, 615, 348,618, 605, 319, 560, 244, 809, 434, 676, 455, 663, 360, 721, 429, 898,377, 780, 400, 817, 239, 837, 458, 619, 666, 435, 899, 128, 678, 350,568, 246, 841, 459, 626, 667, 437, 592, 408, 621, 466, 737, 364, 782,247, 679, 572, 351, 788, 412, 783, 461, 627, 708, 250, 682, 366, 804,467, 790, 192, 669, 600, 441, 683, 372, 629, 791, 424, 710, 251, 574,482, 794, 690, 469, 806, 367, 901, 604, 414, 711, 374, 656, 428, 575,633, 415, 253, 795, 685, 483, 616, 473, 849, 691, 224, 807, 606, 375,810, 430, 905, 836, 456, 797, 378, 693, 436, 620, 664, 485, 722, 320,607, 717, 431, 811, 913, 240, 838, 379, 865, 818, 460, 813, 668, 438,723, 622, 489, 680, 381, 697, 628, 462, 738, 839, 497, 670, 623, 352,819, 725, 439, 842, 630, 468, 684, 843, 248, 739, 442, 900, 821, 463,784, 929, 470, 729, 850, 671, 443, 631, 792, 252, 845, 902, 368, 686,634, 254, 712, 692, 471, 741, 906, 416, 796, 903, 484, 687, 825, 635,445, 866, 376, 576, 694, 474, 851, 808, 961, 486, 853, 798, 475, 907,745, 255, 637, 718, 695, 432, 799, 812, 380, 867, 724, 914, 487, 698,909, 477, 753, 719, 814, 490, 857, 915, 840, 440, 869, 820, 608, 491,930, 726, 382, 699, 917, 624, 498, 815, 740, 873, 493, 727, 701, 844,464, 822, 931, 921, 383, 730, 962, 742, 499, 672, 933, 904, 444, 846,823, 881, 852, 446, 632, 826, 731, 472, 847, 743, 746, 447, 688, 636,827, 854, 256, 733, 937, 963, 476, 908, 868, 800, 696, 501, 747, 638,855, 829, 488, 754, 858, 965, 910, 505, 916, 720, 945, 478, 870, 700,749, 639, 755, 492, 911, 859, 969, 871, 479, 918, 816, 702, 728, 384,874, 757, 861, 932, 919, 494, 977, 922, 824, 875, 732, 500, 934, 882,703, 761, 495, 744, 923, 848, 877, 935, 828, 502, 734, 883, 938, 748,964, 448, 993, 925, 856, 735, 830, 885, 503, 939, 966, 750, 860, 831,756, 506, 946, 967, 872, 941, 889, 912, 507, 751, 970, 947, 640, 862,758, 971, 480, 949, 920, 978, 876, 759, 863, 924, 509, 973, 762, 878,979, 704, 953, 884, 936, 496, 763, 994, 981, 879, 926, 886, 940, 927,504, 765, 995, 985, 736, 887, 942, 968, 890, 948, 997, 508, 832, 943,752, 891, 972, 950, 1001, 893, 974, 1009, 864, 510, 951, 980, 760, 954,975, 982, 955, 764, 880, 766, 983, 928, 996, 511, 957, 888, 986, 998,987, 767, 944, 892, 999, 989, 1002, 952, 1003, 894, 1010, 1005, 976,512, 895, 1011, 956, 958, 984, 959, 768, 988, 1013, 1000, 1017, 990,1004, 991, 896, 1006, 1012, 1007, 1014, 960, 1015, 1018, 1019, 992,1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S5: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514,14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261,517, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273,193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77,83, 138, 57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44,99, 141, 31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577,76, 267, 105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525,84, 58, 113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100,140, 197, 87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143,91, 201, 546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209,268, 386, 325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387,578, 329, 549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115,196, 170, 157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178,282, 92, 553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121,645, 104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210,285, 181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534,401, 306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307,548, 330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159,609, 417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580,122, 200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394,284, 773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395,233, 204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563,287, 300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207,328, 646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302,228, 303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189,450, 332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774,611, 658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543,335, 124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356,674, 584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779,564, 404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588,781, 706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567,304, 598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220,648, 312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191,571, 370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365,423, 336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454,834, 318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434,560, 238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662,429, 780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458,817, 246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621,466, 737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783,366, 790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791,372, 710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711,374, 575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430,795, 865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664,722, 320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668,240, 818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628,248, 900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670,463, 739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368,671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796,416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907,471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487,753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915,440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740,930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742,846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501,446, 933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638,908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800,700, 494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479,384, 911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923,875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848,993, 448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830,966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751,872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863,762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994,926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890,948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954,510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928,511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005,894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959,1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896,1014, 992, 1019, 960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S6: [1, 2, 3, 5, 9, 17, 33, 4, 257, 513, 6, 65, 7, 10, 11, 129,18, 13, 19, 34, 21, 35, 25, 66, 37, 258, 67, 8, 12, 130, 41, 69, 514,14, 20, 131, 49, 15, 73, 259, 22, 133, 36, 81, 23, 26, 137, 38, 97, 515,261, 145, 27, 39, 68, 42, 29, 161, 70, 265, 43, 50, 75, 517, 193, 71,45, 273, 132, 16, 74, 51, 24, 53, 289, 521, 134, 82, 77, 135, 28, 57,260, 83, 138, 40, 529, 98, 262, 30, 85, 139, 146, 31, 321, 545, 99, 44,89, 141, 263, 147, 72, 46, 516, 101, 266, 162, 52, 149, 47, 267, 769,76, 163, 105, 385, 54, 153, 78, 518, 194, 274, 165, 55, 84, 269, 577,136, 58, 113, 275, 195, 79, 519, 169, 290, 59, 86, 61, 277, 522, 87,140, 291, 100, 197, 523, 90, 281, 142, 177, 322, 91, 641, 102, 148, 293,143, 32, 530, 323, 103, 106, 264, 525, 201, 150, 48, 268, 93, 531, 209,386, 164, 151, 546, 297, 107, 56, 325, 533, 154, 225, 270, 114, 80, 547,276, 166, 109, 537, 387, 155, 60, 305, 578, 115, 167, 271, 157, 549,329, 196, 170, 278, 770, 198, 171, 389, 579, 117, 292, 88, 62, 520, 337,178, 63, 524, 279, 92, 282, 144, 642, 199, 393, 104, 553, 294, 173, 353,581, 202, 121, 401, 526, 179, 283, 94, 532, 152, 295, 203, 643, 324,108, 298, 561, 181, 210, 285, 527, 95, 417, 205, 585, 326, 185, 771,299, 211, 110, 534, 306, 156, 331, 645, 116, 449, 548, 111, 327, 168,593, 301, 213, 535, 388, 158, 272, 538, 226, 118, 649, 330, 172, 307,550, 227, 280, 609, 217, 309, 773, 159, 390, 657, 119, 338, 174, 539,333, 122, 551, 391, 200, 580, 180, 229, 554, 284, 123, 541, 313, 64,673, 339, 175, 394, 582, 233, 296, 777, 204, 354, 555, 182, 286, 562,341, 587, 206, 395, 705, 125, 402, 583, 183, 287, 557, 212, 355, 785,186, 300, 644, 207, 345, 528, 96, 397, 586, 187, 563, 403, 328, 536,241, 302, 565, 214, 801, 357, 112, 646, 418, 228, 594, 308, 589, 405,215, 647, 303, 189, 540, 332, 569, 160, 419, 772, 361, 218, 595, 310,650, 230, 409, 552, 334, 610, 120, 450, 774, 219, 542, 421, 176, 597,311, 651, 340, 658, 231, 392, 543, 314, 833, 124, 369, 611, 221, 556,451, 335, 601, 234, 653, 425, 775, 235, 315, 659, 342, 584, 126, 558,317, 613, 343, 184, 778, 396, 674, 356, 564, 242, 453, 661, 208, 559,346, 779, 398, 588, 188, 433, 675, 347, 617, 237, 897, 358, 566, 404,665, 127, 590, 399, 288, 706, 243, 786, 359, 677, 362, 567, 216, 596,457, 781, 406, 648, 190, 570, 304, 625, 349, 245, 787, 465, 707, 420,591, 407, 681, 220, 802, 363, 571, 312, 598, 191, 573, 410, 789, 481,599, 232, 652, 370, 803, 336, 612, 422, 709, 249, 602, 365, 793, 411,222, 316, 654, 371, 689, 423, 834, 236, 603, 413, 614, 452, 660, 426,805, 223, 655, 454, 544, 427, 835, 128, 615, 373, 618, 344, 776, 318,713, 238, 662, 560, 434, 780, 319, 605, 348, 721, 244, 898, 400, 676,455, 663, 360, 809, 429, 619, 239, 568, 458, 837, 666, 377, 737, 435,782, 246, 626, 350, 592, 408, 788, 678, 459, 621, 192, 899, 364, 667,437, 572, 466, 817, 627, 351, 679, 247, 783, 461, 669, 841, 441, 708,467, 682, 366, 790, 250, 710, 683, 412, 901, 372, 629, 804, 367, 600,424, 574, 251, 849, 690, 469, 575, 414, 791, 604, 482, 794, 374, 656,428, 711, 905, 253, 616, 483, 806, 685, 473, 865, 415, 714, 633, 375,913, 691, 224, 795, 430, 606, 664, 378, 807, 456, 715, 836, 436, 620,810, 485, 693, 379, 722, 797, 240, 607, 929, 320, 717, 431, 838, 697,489, 811, 723, 460, 622, 818, 438, 668, 462, 843, 628, 248, 961, 623,381, 839, 680, 439, 813, 725, 468, 900, 670, 442, 784, 738, 463, 630,352, 842, 684, 252, 819, 739, 443, 792, 729, 821, 497, 671, 902, 470,631, 850, 368, 686, 845, 484, 634, 903, 471, 712, 692, 445, 741, 796,416, 635, 825, 576, 254, 851, 687, 474, 906, 745, 486, 808, 716, 866,376, 694, 798, 475, 853, 718, 432, 907, 637, 914, 487, 695, 799, 380,724, 867, 698, 477, 812, 719, 490, 857, 608, 909, 255, 699, 915, 840,491, 753, 814, 726, 382, 869, 624, 440, 930, 740, 820, 498, 917, 727,815, 464, 701, 844, 672, 444, 931, 873, 730, 493, 822, 742, 921, 383,846, 632, 962, 499, 731, 933, 688, 823, 472, 852, 743, 904, 446, 826,636, 881, 501, 733, 963, 847, 746, 256, 937, 747, 827, 476, 854, 638,829, 855, 447, 696, 908, 868, 754, 488, 965, 720, 858, 910, 505, 700,945, 859, 478, 749, 870, 916, 639, 911, 492, 800, 755, 871, 874, 479,728, 969, 918, 702, 384, 816, 861, 757, 977, 932, 494, 919, 732, 875,824, 703, 500, 922, 993, 744, 882, 495, 848, 934, 761, 877, 923, 734,502, 828, 883, 935, 748, 925, 448, 964, 938, 735, 966, 939, 640, 503,885, 856, 830, 750, 946, 831, 506, 860, 756, 912, 967, 872, 941, 507,751, 970, 889, 947, 758, 862, 920, 509, 971, 704, 876, 949, 978, 863,759, 480, 973, 953, 979, 878, 762, 924, 884, 879, 496, 936, 763, 981,926, 994, 886, 940, 765, 504, 995, 985, 927, 887, 736, 942, 890, 968,948, 997, 508, 891, 752, 832, 943, 1001, 972, 950, 974, 760, 893, 951,510, 980, 954, 975, 864, 764, 955, 1009, 982, 880, 996, 983, 957, 928,511, 766, 986, 998, 888, 987, 944, 999, 892, 989, 1002, 767, 1003, 894,952, 1010, 976, 956, 512, 1005, 895, 1011, 984, 958, 1013, 768, 988,959, 1000, 1017, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 960, 1015,1018, 1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S7: [1, 2, 3, 5, 9, 17, 4, 33, 6, 7, 65, 10, 11, 18, 13, 19,129, 34, 21, 35, 25, 8, 37, 66, 257, 67, 12, 41, 69, 14, 20, 49, 130,15, 73, 22, 131, 513, 36, 23, 133, 81, 26, 38, 27, 258, 137, 39, 68, 97,42, 259, 29, 145, 43, 70, 261, 50, 71, 16, 45, 74, 51, 265, 132, 161,514, 75, 24, 53, 134, 82, 515, 273, 77, 135, 83, 28, 57, 193, 138, 517,40, 98, 85, 260, 30, 139, 289, 521, 146, 99, 44, 31, 262, 141, 89, 147,72, 101, 46, 263, 529, 321, 52, 266, 162, 149, 47, 76, 105, 267, 54,163, 516, 274, 153, 545, 78, 55, 269, 136, 165, 84, 113, 58, 194, 275,518, 385, 79, 59, 86, 195, 140, 290, 169, 519, 277, 577, 522, 100, 87,32, 291, 61, 197, 142, 90, 523, 281, 148, 177, 102, 264, 143, 293, 530,91, 322, 201, 525, 150, 103, 48, 531, 106, 641, 323, 93, 268, 297, 164,151, 209, 154, 546, 107, 533, 325, 56, 270, 166, 114, 276, 155, 547,305, 386, 80, 109, 271, 537, 167, 115, 329, 60, 196, 225, 170, 520, 278,387, 157, 549, 578, 769, 88, 117, 292, 62, 171, 198, 279, 389, 579, 337,524, 282, 553, 178, 63, 199, 144, 294, 173, 92, 121, 202, 283, 581, 526,179, 393, 104, 295, 532, 561, 642, 324, 94, 203, 353, 298, 527, 285,152, 181, 585, 210, 108, 534, 643, 401, 95, 299, 326, 205, 211, 156,548, 306, 185, 535, 110, 645, 327, 272, 593, 301, 538, 168, 116, 330,226, 307, 213, 388, 158, 550, 417, 111, 539, 770, 649, 331, 118, 227,172, 280, 159, 551, 309, 390, 580, 338, 217, 609, 554, 771, 541, 119,333, 64, 200, 229, 174, 391, 122, 657, 339, 284, 555, 313, 582, 449,180, 394, 773, 296, 175, 562, 123, 204, 354, 233, 583, 341, 528, 286,395, 557, 182, 586, 563, 777, 644, 402, 96, 673, 355, 125, 300, 206,287, 183, 397, 587, 345, 212, 241, 186, 536, 403, 565, 646, 328, 207,357, 594, 302, 785, 589, 308, 187, 214, 418, 112, 647, 405, 595, 303,540, 569, 705, 650, 332, 361, 228, 215, 160, 552, 310, 419, 189, 218,610, 597, 772, 542, 651, 409, 801, 120, 334, 230, 311, 392, 421, 658,340, 219, 611, 369, 556, 314, 450, 543, 774, 653, 335, 601, 231, 176,124, 659, 234, 315, 584, 342, 451, 221, 613, 396, 558, 425, 775, 833,564, 778, 674, 356, 126, 235, 661, 343, 288, 559, 317, 453, 184, 398,588, 346, 617, 242, 779, 404, 566, 675, 433, 127, 208, 358, 237, 399,786, 665, 347, 590, 243, 457, 188, 567, 781, 648, 406, 677, 359, 596,304, 625, 570, 706, 787, 362, 897, 591, 349, 216, 245, 420, 190, 407,571, 598, 707, 465, 652, 410, 802, 681, 363, 789, 312, 191, 422, 220,612, 370, 249, 599, 544, 411, 803, 573, 709, 654, 336, 365, 602, 232,793, 423, 660, 689, 371, 316, 452, 222, 614, 481, 426, 776, 655, 413,805, 603, 834, 713, 236, 662, 344, 223, 615, 373, 560, 318, 427, 454,618, 835, 605, 780, 809, 676, 434, 128, 663, 238, 319, 455, 400, 721,429, 666, 348, 619, 377, 244, 458, 837, 568, 782, 435, 678, 360, 239,626, 788, 667, 817, 898, 592, 350, 459, 621, 246, 783, 408, 679, 437,627, 841, 572, 708, 466, 737, 682, 364, 790, 899, 669, 351, 247, 461,192, 250, 600, 467, 629, 412, 804, 574, 683, 441, 710, 791, 366, 901,849, 794, 424, 690, 372, 251, 482, 575, 711, 469, 656, 414, 806, 685,367, 604, 633, 714, 795, 691, 905, 224, 616, 374, 483, 253, 428, 415,807, 836, 606, 715, 473, 865, 810, 797, 664, 693, 375, 320, 456, 485,722, 430, 620, 378, 913, 607, 811, 838, 717, 436, 240, 723, 431, 668,818, 697, 379, 460, 622, 489, 839, 784, 813, 680, 438, 628, 842, 738,819, 725, 900, 670, 352, 929, 623, 381, 248, 462, 439, 843, 468, 630,739, 497, 684, 442, 792, 671, 821, 902, 463, 850, 729, 252, 631, 845,576, 443, 712, 470, 741, 686, 368, 903, 634, 851, 796, 825, 961, 692,906, 484, 254, 471, 416, 808, 687, 445, 635, 716, 474, 866, 745, 853,798, 907, 694, 376, 255, 486, 914, 608, 475, 867, 637, 812, 718, 799,695, 909, 857, 487, 724, 432, 753, 698, 380, 915, 490, 840, 719, 477,869, 814, 820, 699, 726, 930, 624, 382, 491, 917, 815, 440, 844, 873,740, 498, 727, 672, 822, 931, 701, 383, 464, 493, 730, 921, 632, 846,499, 444, 742, 823, 904, 933, 852, 731, 881, 826, 962, 847, 472, 743,501, 688, 446, 636, 746, 827, 854, 963, 733, 908, 937, 256, 447, 476,868, 638, 747, 505, 855, 800, 829, 965, 696, 910, 858, 488, 754, 916,945, 639, 720, 478, 870, 749, 911, 859, 755, 969, 700, 492, 918, 479,871, 816, 874, 861, 728, 757, 932, 702, 384, 919, 494, 977, 922, 875,500, 824, 703, 934, 495, 732, 882, 761, 923, 848, 877, 744, 502, 935,883, 828, 964, 734, 993, 938, 925, 503, 448, 748, 506, 856, 735, 885,830, 939, 966, 946, 640, 507, 750, 831, 967, 912, 941, 860, 889, 756,970, 947, 480, 872, 751, 509, 862, 971, 758, 920, 949, 978, 876, 863,759, 973, 704, 496, 762, 979, 924, 953, 878, 936, 884, 763, 994, 981,926, 879, 504, 736, 886, 995, 765, 940, 927, 985, 508, 887, 832, 968,997, 942, 890, 948, 752, 510, 943, 891, 972, 1001, 950, 511, 864, 893,760, 974, 951, 980, 1009, 954, 975, 764, 955, 982, 880, 996, 766, 983,928, 957, 986, 888, 767, 998, 987, 999, 944, 892, 1002, 989, 512, 894,1003, 952, 1010, 895, 976, 1005, 1011, 956, 984, 1013, 958, 768, 959,988, 1017, 1000, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 1015, 960,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S8: [1, 2, 3, 5, 9, 17, 33, 4, 6, 7, 65, 10, 11, 18, 13, 129,19, 34, 21, 35, 25, 257, 37, 8, 66, 67, 41, 12, 69, 14, 130, 49, 20, 15,73, 513, 131, 22, 133, 36, 23, 81, 26, 258, 38, 137, 27, 259, 39, 97,68, 42, 29, 145, 261, 70, 43, 50, 71, 265, 45, 16, 74, 514, 161, 132,51, 75, 515, 134, 273, 53, 24, 82, 77, 517, 135, 193, 83, 138, 57, 28,289, 260, 40, 98, 521, 139, 85, 30, 146, 262, 99, 141, 44, 31, 89, 529,147, 263, 321, 101, 72, 266, 46, 162, 149, 52, 267, 47, 105, 545, 76,516, 163, 274, 54, 153, 269, 385, 78, 518, 165, 136, 275, 194, 55, 113,84, 58, 79, 519, 577, 290, 195, 277, 522, 169, 140, 86, 59, 291, 197,100, 523, 87, 142, 281, 61, 32, 90, 530, 177, 148, 293, 264, 322, 102,525, 143, 201, 641, 91, 531, 150, 323, 103, 297, 268, 48, 106, 546, 164,93, 533, 151, 209, 325, 154, 270, 107, 547, 386, 166, 305, 276, 56, 114,537, 155, 271, 329, 769, 109, 549, 387, 80, 520, 167, 578, 225, 196,278, 115, 170, 157, 60, 579, 389, 292, 553, 279, 198, 524, 337, 171,117, 88, 282, 62, 178, 581, 294, 199, 393, 526, 173, 144, 283, 202, 642,63, 121, 561, 92, 532, 179, 295, 353, 324, 104, 527, 585, 298, 203, 643,285, 401, 94, 534, 181, 152, 210, 326, 299, 205, 108, 645, 548, 95, 535,593, 306, 211, 538, 327, 185, 156, 301, 272, 330, 770, 417, 110, 550,388, 168, 307, 226, 649, 213, 116, 539, 158, 331, 771, 111, 551, 609,580, 390, 227, 309, 554, 280, 338, 172, 118, 541, 159, 217, 657, 333,773, 391, 449, 582, 229, 555, 200, 339, 394, 119, 174, 313, 284, 64,122, 562, 180, 583, 296, 354, 777, 557, 395, 528, 341, 175, 586, 233,673, 204, 644, 286, 123, 563, 402, 182, 355, 587, 397, 300, 287, 206,646, 345, 785, 125, 565, 403, 96, 536, 183, 594, 241, 212, 357, 328,186, 589, 302, 207, 647, 705, 418, 595, 405, 308, 650, 569, 214, 540,187, 303, 361, 801, 332, 772, 419, 112, 552, 610, 228, 651, 597, 310,215, 409, 542, 189, 160, 218, 658, 334, 774, 611, 421, 392, 450, 311,230, 653, 556, 369, 340, 120, 543, 601, 314, 219, 659, 335, 775, 833,613, 451, 584, 231, 778, 425, 558, 396, 342, 176, 315, 234, 674, 221,124, 661, 564, 453, 356, 779, 559, 617, 343, 588, 398, 235, 675, 317,288, 346, 786, 433, 126, 566, 404, 184, 242, 665, 358, 781, 399, 457,897, 590, 237, 677, 208, 648, 347, 787, 706, 127, 567, 625, 596, 406,243, 570, 359, 188, 591, 304, 362, 802, 707, 420, 349, 789, 681, 407,652, 465, 598, 245, 571, 216, 410, 190, 363, 803, 709, 612, 422, 599,312, 654, 370, 793, 573, 411, 544, 191, 602, 249, 689, 220, 660, 365,805, 336, 776, 423, 834, 481, 614, 452, 232, 655, 371, 713, 426, 603,413, 316, 222, 662, 835, 615, 809, 454, 780, 427, 560, 373, 618, 344,236, 676, 605, 318, 223, 663, 721, 434, 837, 666, 455, 782, 619, 429,400, 458, 898, 319, 238, 678, 377, 817, 348, 788, 435, 128, 568, 626,244, 667, 360, 783, 841, 621, 459, 899, 592, 239, 679, 737, 708, 350,790, 627, 437, 682, 408, 466, 246, 669, 572, 461, 364, 901, 804, 351,791, 710, 849, 683, 629, 467, 600, 247, 794, 441, 574, 412, 192, 250,690, 366, 806, 711, 424, 482, 905, 685, 656, 469, 372, 795, 714, 575,633, 604, 414, 251, 691, 367, 807, 865, 836, 483, 616, 810, 715, 428,374, 797, 415, 473, 913, 606, 253, 693, 224, 664, 722, 838, 485, 811,456, 375, 717, 620, 430, 607, 320, 378, 818, 723, 436, 839, 697, 668,813, 784, 431, 842, 489, 929, 622, 460, 900, 240, 680, 379, 819, 738,725, 628, 438, 670, 843, 623, 462, 902, 739, 381, 821, 352, 792, 439,850, 684, 497, 630, 468, 248, 671, 729, 442, 845, 463, 903, 961, 741,712, 851, 906, 631, 686, 825, 470, 796, 443, 576, 634, 252, 692, 368,808, 866, 484, 907, 853, 687, 745, 471, 716, 798, 635, 445, 416, 474,914, 254, 694, 867, 486, 909, 812, 376, 799, 718, 857, 637, 475, 915,608, 255, 695, 753, 724, 869, 840, 698, 487, 814, 719, 432, 490, 930,477, 380, 917, 820, 726, 699, 815, 873, 844, 491, 931, 624, 740, 382,822, 727, 440, 498, 921, 701, 672, 730, 846, 493, 933, 464, 904, 962,383, 823, 742, 881, 852, 499, 632, 826, 731, 444, 847, 963, 743, 937,908, 854, 688, 501, 827, 746, 472, 733, 636, 446, 965, 868, 855, 910,747, 829, 800, 447, 858, 505, 945, 638, 476, 916, 256, 696, 754, 870,488, 911, 969, 749, 720, 859, 639, 478, 918, 755, 871, 700, 816, 874,492, 932, 861, 479, 919, 977, 757, 728, 922, 702, 875, 494, 934, 384,824, 882, 500, 923, 703, 761, 732, 877, 848, 495, 935, 993, 964, 744,883, 938, 502, 925, 828, 734, 966, 939, 885, 856, 503, 748, 830, 735,448, 506, 946, 967, 941, 912, 970, 831, 750, 889, 860, 507, 947, 640,756, 872, 971, 751, 862, 509, 949, 480, 920, 978, 758, 973, 876, 863,979, 759, 953, 924, 704, 762, 878, 496, 936, 994, 981, 884, 926, 763,879, 995, 940, 886, 504, 927, 985, 765, 736, 997, 968, 887, 942, 832,890, 508, 948, 943, 1001, 972, 752, 891, 510, 950, 974, 893, 864, 511,951, 1009, 980, 760, 954, 975, 982, 955, 764, 880, 996, 983, 957, 928,986, 766, 998, 888, 987, 767, 999, 944, 1002, 989, 892, 1003, 894, 512,952, 1010, 1005, 976, 895, 1011, 956, 1013, 984, 958, 959, 1017, 988,768, 1000, 990, 1004, 991, 1006, 896, 1012, 1007, 1014, 1015, 960, 1018,1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S9: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 41, 130, 12, 69, 49, 14,131, 20, 15, 73, 258, 22, 133, 23, 81, 36, 259, 26, 137, 97, 261, 38,145, 27, 514, 39, 515, 265, 68, 29, 42, 161, 43, 45, 517, 50, 70, 273,193, 521, 529, 16, 71, 132, 74, 51, 289, 545, 24, 75, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 30, 85, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 101, 266, 72, 46, 162, 518, 577, 519,52, 149, 522, 47, 105, 267, 163, 274, 523, 641, 76, 54, 153, 113, 269,194, 165, 275, 78, 55, 530, 525, 531, 136, 58, 84, 195, 290, 79, 169,277, 59, 86, 61, 87, 140, 100, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 48, 322, 293, 201, 323,578, 150, 297, 93, 106, 209, 549, 579, 268, 386, 325, 305, 164, 151, 56,107, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155,276, 60, 271, 115, 167, 524, 581, 561, 88, 196, 62, 157, 170, 278, 292,279, 198, 171, 117, 178, 282, 526, 643, 532, 527, 92, 63, 585, 770, 144,389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534, 645,535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210, 538,95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110, 156,327, 116, 111, 773, 550, 657, 539, 551, 168, 213, 307, 330, 158, 226,118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119,541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 175,394, 284, 123, 233, 341, 449, 354, 395, 204, 182, 673, 555, 557, 562,582, 296, 286, 125, 183, 206, 785, 705, 64, 287, 528, 583, 644, 586,563, 300, 355, 186, 402, 212, 397, 345, 207, 302, 801, 96, 187, 241,536, 587, 565, 646, 594, 328, 403, 214, 357, 308, 303, 833, 589, 647,112, 540, 569, 595, 650, 772, 160, 418, 332, 228, 405, 310, 215, 552,610, 897, 120, 189, 361, 419, 409, 369, 218, 450, 421, 542, 597, 651,774, 658, 311, 230, 334, 219, 543, 611, 176, 392, 124, 314, 231, 340,335, 221, 451, 425, 315, 556, 601, 653, 234, 775, 659, 613, 126, 288,184, 342, 396, 356, 778, 584, 558, 674, 343, 235, 564, 661, 559, 617,779, 675, 398, 317, 346, 242, 208, 404, 358, 188, 237, 786, 127, 588,566, 665, 625, 781, 304, 453, 433, 243, 347, 706, 399, 677, 787, 590,567, 648, 216, 406, 359, 570, 596, 362, 707, 190, 457, 349, 420, 802,407, 245, 410, 363, 591, 681, 789, 571, 598, 220, 573, 422, 370, 599,652, 612, 709, 602, 803, 312, 793, 191, 411, 654, 689, 603, 232, 249,365, 465, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 236,223, 344, 373, 427, 544, 481, 615, 454, 776, 318, 238, 434, 560, 834,805, 713, 835, 662, 809, 605, 618, 721, 780, 348, 898, 319, 455, 837,817, 676, 663, 244, 429, 400, 360, 239, 377, 458, 435, 350, 568, 619,666, 737, 899, 841, 782, 626, 246, 459, 408, 592, 678, 621, 667, 788,572, 783, 627, 679, 128, 364, 351, 247, 437, 466, 412, 461, 250, 366,467, 600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 424, 690,794, 604, 575, 192, 372, 441, 251, 414, 367, 469, 482, 374, 656, 901,806, 711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606,224, 375, 483, 664, 836, 905, 810, 715, 620, 797, 693, 430, 456, 473,378, 722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 436, 320, 813,240, 622, 431, 485, 460, 379, 668, 839, 438, 489, 628, 623, 462, 381,439, 352, 248, 680, 725, 819, 842, 670, 738, 630, 468, 442, 252, 463,497, 443, 368, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631,792, 845, 902, 686, 470, 634, 712, 471, 692, 741, 851, 825, 903, 687,416, 484, 254, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866,907, 716, 694, 808, 475, 798, 637, 695, 432, 718, 576, 799, 812, 867,380, 487, 698, 914, 255, 724, 909, 857, 719, 477, 814, 608, 490, 699,753, 840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 464, 383, 498,672, 930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730,444, 493, 499, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904,636, 826, 743, 852, 847, 733, 963, 937, 827, 746, 476, 501, 638, 488,505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720, 916,870, 700, 749, 639, 816, 965, 945, 755, 859, 911, 256, 478, 492, 479,728, 918, 871, 494, 874, 702, 969, 500, 861, 495, 932, 919, 757, 922,875, 732, 934, 882, 824, 703, 502, 923, 384, 744, 761, 877, 977, 848,935, 828, 734, 883, 938, 964, 925, 748, 735, 856, 885, 939, 993, 448,503, 506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872,751, 889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759,949, 978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504,926, 879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985,508, 890, 948, 832, 752, 943, 997, 972, 891, 950, 1001, 974, 893, 510,951, 864, 760, 511, 980, 954, 764, 975, 1009, 955, 880, 982, 983, 928,996, 766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 989, 1002, 952,1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988, 1013,1000, 1017, 512, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960,1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S10: [1, 2, 3, 5, 9, 17, 33, 4, 257, 513, 6, 65, 7, 10, 11, 18,129, 13, 19, 34, 21, 35, 25, 37, 66, 258, 8, 67, 41, 12, 69, 130, 514,14, 49, 20, 73, 131, 15, 259, 22, 133, 36, 81, 23, 26, 137, 38, 27, 515,261, 97, 39, 68, 42, 145, 29, 70, 43, 265, 50, 71, 161, 517, 45, 74,132, 273, 16, 51, 75, 134, 53, 82, 289, 521, 24, 193, 77, 135, 83, 138,260, 57, 28, 98, 529, 139, 262, 40, 85, 146, 30, 99, 321, 545, 141, 44,89, 147, 263, 31, 101, 72, 516, 162, 266, 46, 149, 52, 105, 267, 769,163, 47, 76, 274, 153, 54, 165, 518, 194, 385, 78, 113, 136, 269, 577,55, 84, 58, 275, 195, 79, 519, 169, 290, 140, 86, 59, 277, 522, 197,100, 291, 87, 142, 523, 177, 281, 61, 90, 293, 148, 530, 32, 201, 322,102, 143, 641, 264, 91, 150, 323, 525, 103, 106, 164, 297, 209, 531, 48,268, 93, 151, 546, 325, 154, 107, 386, 533, 166, 114, 270, 155, 56, 547,305, 225, 109, 537, 276, 167, 196, 329, 549, 80, 115, 387, 170, 578,271, 157, 60, 278, 770, 198, 171, 389, 520, 117, 292, 88, 178, 579, 337,62, 199, 553, 279, 173, 282, 202, 524, 121, 393, 144, 581, 294, 179,283, 642, 63, 92, 353, 526, 203, 295, 104, 561, 181, 324, 210, 532, 298,94, 401, 585, 152, 205, 285, 643, 108, 326, 211, 527, 299, 95, 771, 306,185, 156, 534, 327, 226, 417, 645, 110, 301, 548, 168, 330, 213, 593,388, 116, 535, 272, 158, 307, 538, 111, 649, 331, 172, 390, 550, 217,309, 539, 118, 338, 773, 159, 280, 609, 229, 449, 200, 551, 333, 119,580, 391, 174, 554, 122, 180, 657, 339, 64, 541, 394, 233, 582, 313,175, 284, 555, 204, 354, 777, 123, 395, 562, 182, 296, 583, 341, 673,206, 402, 557, 241, 286, 586, 125, 355, 644, 183, 397, 785, 212, 300,528, 96, 345, 563, 186, 403, 587, 207, 646, 287, 357, 565, 214, 328,594, 187, 801, 418, 536, 302, 112, 705, 405, 589, 308, 215, 647, 361,189, 595, 419, 650, 218, 303, 772, 332, 160, 569, 409, 540, 230, 310,610, 421, 651, 219, 450, 774, 120, 552, 334, 231, 597, 369, 658, 392,542, 234, 311, 611, 340, 833, 176, 314, 653, 221, 556, 451, 335, 601,124, 659, 425, 775, 235, 396, 543, 342, 613, 242, 584, 315, 674, 453,126, 778, 356, 558, 343, 661, 184, 398, 564, 237, 617, 433, 779, 675,208, 346, 559, 404, 588, 243, 786, 288, 665, 457, 566, 127, 677, 358,399, 706, 188, 897, 347, 590, 406, 625, 245, 648, 359, 781, 362, 567,216, 596, 420, 570, 465, 190, 787, 304, 707, 349, 591, 407, 681, 249,802, 410, 652, 363, 598, 191, 571, 422, 789, 370, 709, 220, 612, 411,803, 312, 599, 481, 654, 232, 689, 365, 793, 423, 222, 452, 573, 336,602, 371, 805, 236, 660, 426, 544, 413, 713, 316, 834, 223, 614, 454,655, 427, 776, 238, 603, 373, 662, 344, 835, 434, 615, 244, 618, 676,809, 455, 721, 429, 560, 128, 780, 458, 605, 377, 663, 400, 837, 435,666, 239, 619, 319, 898, 678, 348, 626, 459, 782, 246, 667, 360, 568,437, 817, 737, 466, 621, 247, 788, 350, 679, 408, 708, 461, 841, 592,364, 627, 250, 899, 467, 682, 783, 351, 669, 441, 572, 412, 790, 192,710, 683, 482, 901, 366, 629, 804, 424, 600, 469, 690, 251, 849, 574,372, 711, 414, 791, 685, 483, 794, 367, 714, 428, 633, 905, 253, 656,473, 806, 691, 374, 795, 415, 575, 604, 485, 865, 715, 224, 807, 456,616, 693, 375, 836, 430, 722, 810, 378, 606, 913, 436, 664, 320, 717,797, 240, 620, 838, 489, 723, 431, 811, 607, 460, 818, 697, 379, 668,839, 438, 738, 462, 929, 622, 248, 813, 680, 497, 842, 725, 381, 900,628, 439, 784, 670, 468, 819, 739, 352, 623, 442, 843, 684, 252, 902,729, 463, 821, 630, 850, 470, 671, 792, 443, 741, 961, 484, 712, 845,368, 631, 903, 471, 686, 634, 445, 692, 851, 474, 576, 906, 745, 254,825, 687, 416, 796, 716, 486, 866, 635, 907, 475, 694, 808, 376, 853,718, 487, 914, 753, 798, 490, 637, 867, 432, 695, 909, 724, 477, 812,608, 380, 857, 698, 915, 255, 719, 799, 869, 491, 726, 840, 699, 498,930, 740, 382, 814, 624, 917, 440, 820, 727, 873, 493, 701, 931, 730,464, 815, 844, 672, 499, 921, 742, 822, 383, 933, 731, 962, 444, 632,846, 743, 881, 501, 904, 746, 823, 472, 852, 688, 826, 446, 733, 963,847, 636, 256, 937, 747, 908, 505, 854, 754, 827, 965, 447, 638, 868,855, 696, 476, 910, 749, 945, 829, 488, 720, 858, 916, 478, 755, 800,969, 639, 870, 492, 911, 700, 859, 918, 479, 757, 871, 874, 728, 494,932, 977, 702, 816, 861, 500, 919, 761, 922, 875, 703, 384, 934, 882,732, 923, 495, 824, 993, 744, 877, 935, 734, 502, 964, 848, 883, 748,938, 503, 925, 828, 735, 966, 939, 750, 506, 885, 856, 946, 756, 830,967, 448, 941, 640, 970, 889, 912, 947, 507, 751, 831, 860, 971, 758,872, 949, 509, 978, 759, 862, 920, 973, 876, 762, 480, 979, 863, 953,924, 704, 994, 878, 936, 496, 981, 763, 884, 926, 995, 879, 940, 765,504, 985, 886, 927, 997, 736, 968, 887, 942, 890, 948, 508, 832, 752,1001, 943, 972, 891, 950, 974, 760, 1009, 893, 510, 951, 980, 864, 954,764, 975, 982, 955, 996, 880, 983, 957, 986, 511, 766, 928, 998, 987,888, 999, 1002, 944, 989, 892, 767, 1003, 1010, 894, 952, 1005, 976,512, 1011, 895, 956, 1013, 984, 958, 768, 1017, 959, 988, 1000, 990,1004, 991, 1006, 1012, 896, 1007, 1014, 1015, 1018, 960, 1019, 1021,992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S11: [1, 2, 3, 5, 9, 17, 4, 33, 6, 7, 65, 10, 11, 18, 13, 19,129, 34, 21, 35, 25, 8, 37, 66, 257, 67, 12, 41, 69, 14, 20, 49, 130,15, 73, 131, 22, 513, 36, 23, 133, 81, 26, 38, 27, 258, 137, 39, 68, 97,42, 259, 29, 145, 43, 70, 261, 50, 71, 16, 45, 74, 51, 265, 132, 161,514, 75, 24, 53, 134, 82, 515, 273, 77, 135, 83, 28, 57, 193, 138, 517,40, 98, 85, 260, 139, 30, 289, 521, 146, 99, 44, 31, 262, 141, 89, 147,72, 101, 46, 263, 529, 321, 52, 266, 162, 149, 47, 76, 105, 267, 163,54, 516, 274, 153, 545, 78, 55, 269, 136, 165, 84, 113, 58, 194, 275,518, 385, 79, 59, 195, 86, 140, 290, 169, 519, 277, 577, 522, 100, 87,32, 291, 61, 197, 142, 90, 523, 281, 148, 177, 102, 264, 143, 293, 530,91, 322, 201, 525, 150, 103, 48, 531, 106, 641, 323, 93, 268, 297, 164,151, 209, 154, 546, 107, 533, 325, 56, 270, 166, 114, 276, 155, 547,305, 386, 80, 109, 271, 537, 167, 115, 329, 60, 196, 225, 170, 520, 387,278, 157, 549, 578, 769, 88, 117, 292, 171, 62, 198, 279, 389, 579, 337,524, 282, 553, 178, 63, 199, 144, 294, 173, 92, 121, 202, 283, 581, 526,179, 393, 104, 295, 532, 561, 642, 324, 203, 94, 353, 298, 527, 285,152, 181, 585, 210, 108, 643, 534, 401, 95, 299, 326, 205, 211, 156,548, 306, 185, 535, 110, 645, 327, 272, 593, 301, 538, 168, 116, 330,226, 307, 213, 388, 158, 550, 417, 111, 539, 770, 649, 331, 227, 118,172, 280, 159, 551, 309, 390, 580, 338, 217, 609, 554, 771, 541, 119,333, 64, 200, 229, 174, 391, 122, 657, 339, 284, 555, 313, 582, 449,180, 394, 773, 296, 175, 562, 123, 204, 354, 233, 583, 341, 528, 395,286, 557, 182, 586, 563, 777, 644, 402, 96, 673, 355, 125, 300, 206,287, 183, 397, 587, 345, 212, 241, 186, 536, 403, 565, 646, 328, 207,357, 594, 302, 785, 589, 308, 187, 214, 418, 112, 647, 405, 595, 303,540, 569, 705, 650, 332, 361, 228, 215, 160, 552, 419, 310, 189, 218,610, 597, 772, 651, 542, 409, 801, 120, 334, 230, 311, 392, 421, 658,340, 219, 611, 369, 556, 314, 450, 543, 774, 653, 335, 601, 231, 176,124, 659, 234, 315, 584, 451, 342, 221, 613, 396, 558, 425, 775, 833,564, 778, 674, 356, 235, 126, 661, 343, 288, 559, 317, 453, 184, 398,588, 346, 617, 242, 779, 404, 675, 566, 433, 127, 208, 358, 237, 399,786, 665, 347, 590, 243, 457, 188, 567, 781, 648, 406, 677, 359, 596,304, 625, 570, 706, 787, 362, 897, 591, 349, 216, 245, 420, 190, 407,571, 707, 598, 465, 652, 410, 802, 681, 363, 789, 312, 191, 422, 220,612, 370, 249, 599, 544, 411, 803, 573, 709, 654, 336, 365, 602, 232,793, 423, 660, 689, 371, 316, 452, 222, 614, 481, 426, 776, 655, 413,805, 603, 834, 713, 236, 662, 344, 223, 615, 373, 560, 427, 318, 454,618, 835, 605, 780, 809, 676, 434, 128, 663, 238, 319, 455, 400, 721,429, 666, 348, 619, 377, 244, 837, 568, 782, 435, 678, 360, 239, 626,788, 667, 817, 898, 592, 350, 621, 246, 783, 408, 679, 437, 627, 841,572, 708, 466, 737, 682, 364, 899, 790, 669, 351, 247, 461, 192, 250,600, 467, 629, 412, 804, 683, 574, 441, 710, 791, 366, 901, 849, 794,424, 690, 372, 251, 482, 575, 711, 469, 656, 414, 806, 685, 367, 604,633, 714, 795, 691, 905, 224, 616, 483, 374, 253, 428, 415, 807, 836,715, 606, 473, 865, 810, 797, 664, 693, 375, 320, 456, 485, 722, 430,620, 378, 913, 607, 811, 838, 717, 436, 240, 723, 431, 668, 818, 697,379, 460, 622, 489, 839, 784, 813, 680, 438, 628, 842, 738, 819, 725,900, 670, 352, 929, 623, 381, 248, 462, 439, 843, 468, 739, 630, 497,684, 442, 792, 671, 821, 902, 463, 850, 729, 252, 631, 845, 576, 443,712, 470, 741, 686, 368, 903, 634, 851, 796, 825, 961, 692, 906, 484,254, 471, 416, 808, 687, 445, 635, 716, 474, 866, 745, 853, 907, 798,694, 376, 255, 486, 914, 608, 475, 867, 637, 812, 718, 799, 695, 909,857, 487, 724, 432, 753, 698, 380, 915, 490, 840, 719, 477, 869, 814,820, 699, 726, 930, 624, 491, 382, 917, 815, 440, 844, 873, 740, 498,727, 672, 931, 822, 701, 383, 464, 493, 730, 921, 632, 846, 499, 444,742, 823, 904, 933, 852, 731, 881, 826, 962, 847, 472, 743, 501, 688,446, 636, 746, 827, 963, 854, 733, 908, 937, 256, 447, 476, 868, 747,638, 505, 855, 800, 829, 965, 696, 910, 858, 488, 754, 916, 945, 639,720, 478, 870, 749, 911, 859, 755, 969, 700, 492, 918, 479, 871, 816,874, 861, 728, 757, 932, 702, 384, 919, 494, 977, 922, 875, 500, 824,703, 934, 495, 732, 882, 761, 923, 848, 877, 744, 502, 935, 883, 828,964, 734, 993, 938, 925, 503, 448, 748, 506, 856, 735, 885, 939, 830,966, 946, 640, 507, 750, 831, 967, 912, 941, 860, 889, 756, 970, 947,480, 872, 751, 509, 971, 862, 758, 920, 949, 978, 876, 863, 759, 973,704, 496, 762, 979, 924, 953, 878, 936, 884, 763, 994, 981, 926, 879,504, 736, 995, 886, 765, 940, 927, 985, 508, 887, 832, 968, 997, 942,890, 948, 752, 510, 943, 891, 972, 1001, 950, 511, 864, 893, 760, 974,951, 980, 1009, 954, 975, 764, 955, 982, 880, 996, 766, 983, 928, 957,986, 888, 767, 998, 987, 999, 944, 892, 1002, 989, 512, 1003, 894, 952,1010, 895, 976, 1005, 1011, 956, 984, 1013, 958, 768, 959, 988, 1017,1000, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 1015, 960, 1018,1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S12: [1, 2, 3, 5, 9, 17, 4, 33, 6, 7, 10, 65, 11, 18, 13, 19,129, 21, 34, 35, 25, 8, 37, 66, 257, 12, 67, 41, 14, 69, 20, 49, 15,130, 73, 22, 131, 23, 36, 513, 133, 26, 81, 38, 27, 137, 39, 258, 29,68, 42, 97, 259, 43, 145, 70, 261, 50, 16, 71, 45, 74, 51, 265, 132,161, 75, 24, 53, 514, 134, 82, 77, 515, 273, 135, 28, 83, 57, 138, 40,193, 517, 30, 85, 98, 139, 260, 289, 31, 44, 521, 99, 146, 141, 89, 262,147, 72, 46, 101, 263, 52, 529, 47, 266, 149, 321, 162, 76, 105, 54,267, 163, 153, 78, 55, 516, 274, 545, 269, 136, 84, 165, 58, 113, 79,275, 194, 518, 59, 385, 86, 140, 195, 169, 519, 277, 290, 32, 87, 61,522, 100, 577, 142, 291, 197, 90, 523, 281, 148, 177, 102, 143, 91, 264,293, 530, 48, 201, 525, 103, 150, 322, 93, 531, 106, 268, 151, 323, 297,164, 641, 107, 154, 56, 209, 533, 546, 270, 325, 166, 114, 155, 80, 276,109, 547, 305, 271, 167, 60, 386, 537, 115, 157, 329, 196, 170, 520,278, 225, 549, 387, 88, 62, 117, 578, 171, 279, 292, 198, 769, 63, 524,389, 282, 579, 337, 553, 178, 144, 199, 92, 173, 121, 294, 283, 202,526, 179, 104, 581, 393, 295, 94, 532, 203, 561, 527, 285, 152, 324,298, 181, 353, 642, 95, 108, 585, 210, 534, 299, 205, 643, 401, 326,156, 211, 185, 535, 110, 548, 306, 272, 327, 301, 168, 645, 538, 116,593, 111, 158, 330, 307, 213, 226, 550, 388, 539, 417, 118, 159, 331,172, 280, 649, 227, 551, 309, 770, 64, 217, 390, 541, 119, 580, 338,554, 609, 333, 200, 771, 174, 229, 122, 391, 284, 339, 555, 313, 180,657, 582, 175, 394, 123, 296, 449, 773, 204, 562, 528, 286, 233, 583,341, 557, 182, 354, 395, 96, 125, 586, 563, 287, 300, 206, 777, 183,355, 644, 402, 673, 397, 587, 345, 212, 186, 536, 241, 207, 565, 403,328, 302, 357, 646, 594, 187, 112, 589, 308, 214, 785, 303, 647, 540,405, 418, 595, 569, 160, 332, 215, 189, 361, 650, 228, 552, 310, 705,419, 218, 542, 120, 597, 610, 651, 409, 334, 311, 772, 230, 801, 219,392, 543, 340, 556, 421, 314, 611, 369, 658, 335, 176, 653, 231, 124,450, 601, 774, 315, 221, 659, 234, 584, 342, 558, 396, 613, 451, 425,775, 126, 564, 288, 235, 343, 559, 317, 778, 184, 356, 661, 833, 674,398, 127, 588, 453, 346, 617, 242, 208, 566, 779, 404, 237, 675, 433,358, 399, 347, 188, 665, 590, 243, 567, 786, 304, 457, 781, 359, 648,406, 596, 677, 570, 625, 591, 349, 216, 787, 190, 362, 245, 706, 407,420, 571, 897, 598, 191, 363, 652, 410, 312, 707, 465, 681, 789, 802,220, 544, 249, 422, 599, 573, 612, 370, 411, 336, 365, 654, 232, 803,709, 602, 423, 316, 222, 793, 371, 660, 689, 614, 655, 413, 452, 426,603, 776, 481, 805, 223, 236, 344, 560, 318, 713, 615, 373, 834, 427,128, 454, 605, 618, 319, 780, 835, 238, 809, 676, 434, 400, 455, 348,429, 619, 377, 666, 244, 568, 721, 239, 458, 782, 435, 360, 837, 678,626, 667, 592, 350, 788, 621, 246, 459, 817, 783, 408, 679, 572, 437,898, 627, 351, 192, 364, 669, 841, 247, 708, 466, 682, 790, 737, 461,899, 250, 600, 574, 412, 629, 467, 683, 441, 791, 366, 804, 710, 251,424, 575, 901, 794, 372, 849, 690, 367, 656, 414, 711, 604, 469, 685,482, 633, 806, 224, 795, 253, 714, 691, 616, 374, 415, 428, 905, 483,807, 606, 320, 715, 473, 797, 375, 664, 836, 810, 693, 865, 456, 430,607, 620, 485, 378, 722, 240, 811, 717, 436, 913, 838, 431, 379, 668,723, 697, 622, 460, 818, 784, 489, 839, 813, 680, 438, 628, 352, 623,381, 670, 842, 248, 819, 725, 738, 462, 439, 900, 929, 630, 671, 843,468, 684, 442, 792, 739, 497, 463, 821, 252, 576, 729, 902, 631, 850,443, 368, 845, 712, 470, 686, 741, 634, 903, 796, 851, 254, 825, 692,416, 471, 687, 445, 906, 484, 635, 808, 961, 255, 716, 474, 798, 376,745, 853, 694, 866, 907, 608, 486, 637, 475, 799, 812, 718, 695, 867,914, 432, 909, 487, 380, 857, 724, 698, 753, 719, 477, 915, 490, 840,814, 869, 699, 624, 382, 820, 726, 491, 815, 440, 917, 930, 383, 672,844, 727, 701, 873, 740, 498, 464, 822, 493, 931, 730, 632, 444, 921,846, 499, 823, 742, 731, 904, 852, 933, 826, 881, 847, 472, 688, 446,743, 636, 501, 962, 256, 827, 733, 746, 854, 447, 908, 963, 937, 638,476, 800, 747, 505, 855, 829, 696, 868, 910, 488, 639, 965, 858, 754,720, 478, 916, 749, 945, 870, 911, 859, 700, 755, 479, 492, 816, 969,871, 918, 384, 861, 728, 702, 874, 757, 919, 494, 932, 703, 875, 922,500, 824, 977, 495, 732, 761, 934, 882, 923, 848, 877, 744, 502, 935,828, 734, 883, 448, 925, 503, 964, 938, 993, 735, 748, 506, 856, 830,885, 939, 640, 966, 507, 831, 750, 946, 912, 967, 860, 941, 889, 756,480, 751, 509, 970, 947, 872, 862, 758, 971, 920, 949, 863, 704, 876,759, 978, 496, 973, 762, 924, 979, 953, 878, 763, 936, 884, 879, 926,504, 981, 994, 736, 765, 886, 927, 940, 995, 508, 832, 985, 887, 968,942, 997, 890, 752, 510, 948, 943, 891, 511, 972, 1001, 950, 864, 893,760, 974, 951, 980, 954, 1009, 975, 764, 955, 880, 982, 766, 928, 983,957, 996, 767, 986, 888, 998, 987, 944, 999, 892, 512, 989, 1002, 894,1003, 952, 895, 1010, 976, 1005, 956, 1011, 984, 958, 1013, 768, 959,988, 1017, 1000, 990, 991, 1004, 896, 1006, 1012, 1007, 1014, 960, 1015,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S13: [1, 2, 3, 5, 9, 17, 33, 4, 6, 513, 65, 7, 10, 11, 129, 18,13, 19, 34, 257, 21, 35, 25, 66, 37, 67, 8, 41, 130, 12, 69, 49, 514,14, 131, 20, 15, 73, 258, 22, 133, 23, 81, 36, 259, 26, 137, 97, 261,515, 38, 145, 27, 39, 265, 68, 29, 42, 161, 43, 45, 50, 70, 517, 273,193, 16, 71, 132, 74, 51, 289, 24, 75, 53, 521, 134, 82, 321, 77, 135,28, 57, 83, 138, 260, 529, 40, 98, 385, 30, 85, 139, 262, 146, 545, 31,99, 44, 89, 141, 263, 147, 101, 516, 266, 72, 46, 162, 52, 149, 47, 518,105, 267, 163, 274, 76, 54, 153, 577, 113, 269, 194, 165, 275, 78, 519,55, 136, 58, 84, 195, 290, 522, 79, 169, 277, 59, 86, 61, 523, 87, 140,100, 197, 90, 641, 291, 281, 142, 177, 91, 102, 530, 148, 143, 32, 103,264, 525, 48, 322, 293, 201, 531, 323, 150, 297, 93, 106, 546, 209, 268,386, 325, 769, 305, 164, 151, 56, 533, 107, 154, 225, 387, 329, 547,270, 114, 80, 537, 166, 109, 155, 276, 578, 60, 271, 115, 167, 549, 88,196, 62, 157, 579, 170, 278, 292, 520, 279, 198, 171, 117, 553, 178,282, 92, 642, 63, 144, 389, 294, 524, 199, 104, 337, 581, 173, 283, 202,561, 121, 179, 295, 526, 94, 152, 324, 643, 393, 298, 203, 532, 108,285, 181, 527, 210, 95, 205, 585, 299, 353, 326, 770, 185, 211, 534,401, 306, 301, 645, 110, 156, 327, 535, 116, 111, 593, 168, 213, 307,548, 330, 158, 771, 226, 118, 172, 538, 331, 227, 649, 388, 309, 217,609, 417, 338, 773, 159, 272, 550, 119, 280, 657, 333, 390, 174, 539,122, 200, 551, 180, 229, 777, 339, 313, 580, 391, 175, 541, 394, 284,554, 123, 233, 341, 673, 449, 354, 555, 395, 204, 557, 182, 296, 562,286, 582, 125, 183, 785, 206, 64, 705, 287, 300, 528, 355, 186, 583,402, 212, 644, 397, 345, 586, 207, 302, 563, 96, 801, 187, 241, 536,328, 403, 587, 214, 565, 357, 308, 646, 303, 112, 594, 160, 833, 418,332, 589, 228, 405, 647, 310, 540, 215, 120, 569, 189, 361, 595, 419,650, 409, 369, 772, 218, 552, 450, 421, 610, 311, 897, 230, 334, 542,219, 597, 176, 651, 392, 124, 774, 314, 658, 231, 340, 543, 335, 611,221, 451, 556, 425, 601, 315, 653, 234, 126, 775, 288, 659, 184, 613,342, 778, 396, 356, 584, 343, 558, 235, 674, 398, 317, 564, 346, 661,242, 559, 208, 617, 404, 358, 779, 188, 675, 237, 786, 127, 588, 304,566, 453, 665, 433, 243, 625, 347, 781, 399, 706, 216, 677, 406, 787,359, 590, 362, 567, 190, 648, 457, 570, 349, 420, 596, 407, 707, 245,802, 410, 591, 363, 681, 220, 789, 422, 571, 370, 598, 312, 573, 191,599, 411, 652, 232, 612, 249, 709, 365, 602, 465, 803, 336, 793, 423,316, 222, 654, 371, 689, 426, 603, 452, 614, 413, 660, 236, 655, 223,544, 344, 615, 373, 776, 427, 560, 481, 834, 454, 805, 318, 713, 238,835, 434, 662, 809, 348, 605, 319, 618, 455, 721, 244, 780, 429, 898,400, 837, 360, 817, 239, 676, 377, 663, 458, 568, 619, 435, 666, 350,737, 246, 899, 459, 841, 408, 782, 626, 128, 592, 364, 678, 351, 621,247, 667, 437, 788, 572, 466, 783, 412, 627, 461, 679, 600, 250, 708,366, 574, 467, 669, 424, 682, 790, 192, 804, 372, 791, 710, 441, 683,251, 629, 414, 690, 794, 367, 604, 469, 575, 656, 482, 901, 374, 806,428, 711, 616, 415, 849, 253, 685, 795, 224, 714, 375, 633, 691, 483,807, 606, 430, 664, 456, 836, 905, 473, 810, 378, 715, 620, 436, 797,693, 320, 722, 240, 607, 717, 431, 811, 865, 485, 838, 460, 697, 723,379, 913, 818, 438, 813, 622, 489, 668, 462, 839, 628, 381, 623, 680,439, 725, 819, 352, 842, 670, 248, 738, 630, 468, 684, 843, 442, 739,252, 900, 821, 463, 729, 929, 497, 850, 671, 784, 443, 631, 792, 368,845, 902, 470, 686, 634, 471, 712, 692, 416, 741, 851, 484, 825, 903,254, 687, 906, 796, 445, 635, 745, 376, 853, 961, 474, 866, 907, 716,486, 694, 808, 475, 798, 637, 432, 695, 718, 576, 380, 799, 812, 487,867, 698, 914, 255, 724, 909, 477, 857, 719, 814, 490, 608, 699, 753,440, 840, 915, 726, 491, 869, 820, 382, 815, 624, 672, 464, 930, 844,740, 383, 917, 822, 727, 498, 632, 701, 873, 444, 931, 921, 881, 493,730, 962, 933, 499, 823, 742, 846, 731, 446, 688, 904, 636, 472, 826,743, 852, 447, 847, 733, 963, 937, 476, 827, 746, 638, 501, 800, 696,854, 908, 488, 868, 855, 747, 910, 505, 829, 858, 754, 720, 256, 916,870, 700, 478, 749, 639, 816, 965, 945, 492, 755, 859, 911, 728, 479,918, 871, 874, 702, 494, 969, 861, 932, 919, 757, 500, 922, 875, 732,934, 882, 495, 824, 703, 923, 744, 502, 761, 877, 977, 848, 935, 828,384, 734, 883, 938, 964, 925, 448, 748, 735, 856, 885, 939, 993, 503,966, 830, 750, 946, 860, 831, 506, 967, 756, 941, 912, 872, 751, 507,889, 970, 947, 862, 758, 971, 920, 480, 640, 876, 863, 759, 949, 978,924, 509, 973, 762, 878, 979, 936, 704, 884, 953, 496, 763, 926, 879,981, 994, 886, 940, 927, 504, 765, 736, 887, 995, 942, 968, 985, 890,948, 832, 508, 752, 943, 997, 972, 891, 950, 1001, 974, 893, 951, 864,510, 760, 980, 954, 764, 975, 1009, 955, 880, 982, 983, 928, 996, 766,511, 957, 888, 986, 998, 987, 944, 892, 999, 767, 989, 1002, 952, 1003,894, 976, 895, 1010, 512, 956, 1005, 1011, 958, 984, 959, 988, 1013,1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960, 1015,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S14: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 37, 67, 25, 257, 21, 66, 35, 8, 130, 41, 12, 73, 133, 514,20, 49, 69, 14, 258, 15, 22, 131, 27, 81, 36, 259, 39, 137, 97, 23, 517,38, 26, 68, 265, 42, 145, 29, 70, 261, 50, 75, 161, 43, 521, 135, 71,45, 82, 273, 16, 51, 132, 193, 74, 24, 515, 138, 53, 289, 77, 134, 83,28, 98, 260, 40, 529, 57, 139, 85, 30, 146, 262, 44, 321, 545, 99, 141,266, 31, 89, 147, 263, 101, 519, 162, 72, 46, 274, 52, 149, 267, 577,47, 76, 105, 165, 194, 54, 163, 516, 385, 269, 78, 153, 55, 86, 525,290, 113, 275, 58, 79, 136, 518, 195, 84, 291, 169, 277, 87, 531, 59,140, 323, 197, 102, 641, 61, 148, 177, 281, 100, 90, 522, 293, 142, 322,201, 91, 546, 32, 143, 103, 264, 530, 48, 387, 106, 297, 209, 523, 154,93, 150, 268, 549, 164, 325, 114, 151, 579, 166, 56, 305, 107, 276, 537,270, 386, 155, 769, 80, 109, 225, 167, 533, 60, 170, 115, 196, 578, 329,271, 278, 88, 547, 157, 117, 389, 520, 337, 292, 279, 198, 642, 62, 178,171, 553, 92, 282, 202, 199, 524, 63, 144, 295, 585, 173, 393, 104, 645,121, 294, 283, 532, 353, 179, 203, 561, 324, 298, 94, 581, 108, 152,210, 526, 285, 181, 401, 770, 95, 205, 299, 527, 327, 156, 534, 306,110, 326, 643, 211, 185, 226, 539, 168, 301, 593, 116, 388, 330, 548,111, 417, 771, 213, 272, 118, 551, 307, 158, 649, 227, 172, 331, 609,338, 390, 535, 309, 217, 550, 122, 391, 538, 159, 280, 333, 580, 119,174, 777, 339, 180, 554, 200, 354, 657, 284, 313, 541, 449, 229, 582,394, 123, 182, 773, 233, 296, 562, 175, 395, 587, 64, 204, 673, 355,555, 402, 341, 647, 125, 286, 583, 183, 300, 557, 241, 212, 594, 287,345, 785, 397, 206, 528, 96, 419, 563, 186, 644, 214, 403, 705, 308,328, 586, 357, 536, 207, 187, 650, 302, 112, 565, 303, 801, 361, 228,589, 418, 160, 646, 405, 595, 310, 215, 540, 450, 332, 610, 120, 772,218, 189, 552, 230, 569, 334, 409, 651, 311, 597, 340, 421, 542, 219,658, 369, 774, 124, 231, 556, 176, 833, 392, 314, 611, 242, 653, 451,335, 778, 221, 543, 342, 601, 425, 315, 659, 184, 775, 234, 613, 356,674, 126, 288, 584, 396, 558, 235, 786, 317, 346, 564, 188, 661, 453,779, 404, 559, 343, 398, 588, 208, 617, 237, 677, 433, 706, 347, 566,362, 675, 127, 243, 897, 358, 781, 406, 590, 216, 665, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 190, 570, 245, 591, 411, 648,220, 707, 312, 596, 363, 803, 465, 681, 407, 789, 422, 599, 232, 571,249, 652, 370, 835, 191, 709, 410, 614, 316, 573, 365, 660, 423, 336,222, 689, 452, 793, 371, 612, 426, 602, 236, 805, 344, 654, 413, 834,481, 713, 223, 603, 318, 544, 454, 655, 427, 615, 373, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 246, 568, 435, 817,458, 619, 350, 788, 466, 782, 898, 364, 667, 408, 592, 128, 621, 247,737, 437, 679, 572, 351, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 430,575, 656, 253, 807, 415, 685, 905, 374, 616, 483, 633, 806, 224, 795,865, 428, 691, 473, 715, 836, 456, 810, 378, 606, 620, 436, 664, 722,320, 797, 431, 693, 913, 240, 607, 717, 462, 811, 485, 839, 668, 379,818, 622, 438, 838, 723, 248, 697, 381, 738, 680, 460, 813, 628, 489,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,446, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742,846, 921, 472, 823, 852, 933, 731, 498, 881, 636, 743, 444, 688, 904,826, 476, 754, 963, 847, 733, 501, 854, 937, 827, 447, 696, 746, 868,638, 488, 800, 908, 747, 829, 494, 858, 700, 965, 916, 478, 855, 910,720, 505, 749, 945, 859, 874, 639, 479, 755, 870, 918, 728, 500, 911,816, 871, 932, 256, 969, 861, 702, 757, 923, 492, 732, 824, 875, 977,919, 503, 934, 744, 761, 882, 495, 703, 922, 828, 877, 935, 848, 506,734, 964, 883, 938, 748, 384, 856, 925, 993, 735, 830, 966, 502, 939,885, 946, 750, 860, 756, 480, 967, 831, 889, 941, 751, 872, 507, 971,912, 758, 947, 970, 862, 978, 448, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926,879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948,832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510,864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511,766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894,1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000,1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992,1019, 960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S15: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 12, 130, 41, 69, 14, 20,131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261, 97,145, 27, 514, 39, 515, 265, 68, 42, 29, 161, 70, 43, 517, 50, 71, 273,193, 521, 529, 45, 16, 132, 74, 51, 289, 545, 24, 75, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 30, 85, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 101, 266, 72, 46, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 163, 274, 523, 641, 105, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 195, 290, 79, 169,277, 59, 86, 61, 87, 140, 100, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 48, 322, 293, 201, 323,578, 150, 297, 93, 106, 209, 549, 579, 268, 386, 325, 305, 164, 151,107, 56, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155,276, 60, 271, 115, 167, 524, 581, 561, 157, 196, 170, 198, 171, 278,292, 279, 117, 88, 62, 178, 282, 526, 643, 532, 527, 63, 92, 585, 770,144, 389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534,645, 535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210,538, 95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110,156, 327, 116, 111, 773, 550, 657, 539, 551, 168, 307, 330, 158, 226,118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119,541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 64,394, 284, 175, 233, 341, 449, 354, 395, 204, 123, 673, 555, 557, 562,582, 296, 286, 182, 206, 125, 785, 705, 183, 287, 528, 583, 644, 586,563, 300, 355, 212, 402, 186, 397, 345, 207, 302, 801, 96, 187, 241,536, 587, 565, 646, 594, 328, 403, 357, 308, 303, 833, 589, 647, 112,540, 569, 595, 650, 772, 228, 418, 332, 215, 405, 310, 189, 552, 610,897, 160, 218, 361, 419, 409, 369, 230, 450, 421, 542, 597, 651, 774,658, 311, 120, 334, 219, 543, 611, 176, 392, 231, 314, 124, 340, 335,221, 451, 425, 315, 556, 601, 653, 234, 775, 659, 613, 235, 288, 453,126, 342, 396, 778, 584, 558, 674, 356, 343, 564, 661, 559, 617, 779,675, 184, 398, 433, 317, 346, 242, 208, 404, 358, 786, 188, 588, 566,665, 625, 781, 237, 127, 243, 347, 399, 706, 216, 677, 787, 590, 567,648, 406, 359, 304, 570, 596, 362, 707, 190, 457, 349, 465, 802, 420,407, 245, 410, 591, 681, 789, 571, 598, 363, 573, 220, 422, 599, 652,612, 709, 602, 803, 370, 793, 312, 191, 654, 689, 603, 411, 232, 249,365, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 481, 236,223, 344, 318, 544, 373, 615, 427, 776, 128, 454, 238, 560, 834, 805,713, 835, 662, 809, 605, 618, 721, 780, 434, 898, 319, 455, 837, 817,676, 663, 348, 429, 400, 377, 244, 239, 458, 435, 360, 568, 619, 666,737, 899, 841, 782, 626, 350, 246, 459, 592, 678, 621, 667, 788, 572,783, 627, 679, 408, 364, 351, 192, 247, 437, 466, 412, 461, 250, 366,600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 441, 690, 794,604, 575, 467, 424, 372, 251, 414, 367, 469, 482, 374, 656, 901, 806,711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606, 483,473, 224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 485, 430, 456,722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 378, 436, 813, 320,622, 240, 431, 460, 379, 668, 839, 489, 438, 628, 623, 462, 381, 439,352, 497, 680, 725, 819, 842, 670, 738, 630, 468, 248, 442, 463, 470,443, 252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631, 792,845, 902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903, 687, 471,416, 484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866, 907,716, 694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812, 867, 432,380, 698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490, 699, 753,840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493, 464, 672,930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730, 383,499, 444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904, 636,826, 743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501, 488, 638,505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720, 916,870, 478, 700, 749, 639, 816, 965, 945, 755, 859, 911, 492, 479, 728,918, 871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932, 919, 757,922, 875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877, 848, 935,828, 734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856, 885, 939,506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872, 751,889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759, 949,978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504, 926,879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985, 508,890, 948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974, 893, 951,864, 760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983, 928, 996,766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989, 1002, 952,1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988, 1013,1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960, 1015,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S16: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 25, 21, 35, 257, 66, 37, 8, 67, 130, 12, 41, 20, 133, 514,14, 69, 49, 73, 258, 15, 22, 131, 81, 27, 36, 259, 137, 39, 97, 23, 517,38, 26, 68, 265, 42, 145, 29, 70, 261, 50, 43, 161, 71, 521, 45, 75, 82,132, 273, 193, 16, 51, 74, 53, 24, 515, 135, 138, 289, 77, 134, 83, 28,98, 260, 40, 529, 57, 139, 85, 30, 146, 262, 44, 321, 545, 99, 141, 266,31, 89, 147, 263, 72, 519, 162, 46, 101, 385, 149, 52, 47, 577, 76, 267,54, 274, 165, 194, 105, 516, 163, 269, 78, 153, 275, 55, 525, 58, 113,136, 86, 79, 290, 518, 195, 84, 291, 59, 277, 169, 531, 100, 140, 323,197, 87, 641, 177, 61, 90, 281, 102, 148, 522, 293, 142, 322, 91, 143,546, 32, 201, 103, 264, 530, 106, 387, 48, 297, 523, 209, 154, 93, 150,268, 164, 537, 769, 533, 325, 151, 56, 166, 107, 305, 114, 578, 276,549, 270, 386, 155, 80, 109, 225, 167, 60, 579, 170, 115, 196, 329, 271,278, 157, 547, 88, 117, 389, 520, 337, 292, 279, 198, 642, 62, 178, 171,553, 92, 282, 199, 63, 524, 144, 173, 295, 585, 202, 393, 104, 645, 121,294, 283, 532, 353, 179, 203, 561, 324, 298, 94, 581, 152, 210, 181,526, 285, 108, 401, 770, 95, 205, 299, 527, 327, 156, 534, 306, 110,326, 643, 211, 116, 185, 539, 168, 301, 593, 226, 388, 330, 548, 111,417, 771, 158, 272, 213, 551, 307, 118, 649, 172, 227, 331, 609, 338,390, 535, 309, 217, 550, 159, 391, 538, 119, 280, 333, 580, 174, 122,777, 339, 200, 554, 180, 657, 354, 284, 541, 313, 449, 582, 229, 394,773, 123, 175, 673, 555, 785, 204, 562, 395, 182, 341, 583, 557, 64,296, 286, 233, 125, 183, 206, 287, 300, 355, 212, 402, 186, 397, 587,345, 594, 647, 528, 96, 563, 241, 644, 207, 705, 328, 586, 403, 536,214, 357, 308, 419, 565, 801, 589, 187, 302, 646, 112, 569, 303, 595,361, 228, 650, 772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 610,597, 552, 651, 160, 230, 120, 334, 409, 311, 421, 219, 542, 369, 658,231, 774, 392, 176, 556, 314, 833, 340, 221, 611, 653, 335, 451, 778,124, 543, 342, 601, 425, 234, 659, 235, 775, 315, 613, 126, 674, 356,184, 584, 288, 558, 396, 564, 661, 242, 779, 559, 317, 346, 617, 675,897, 404, 343, 398, 188, 453, 208, 433, 786, 237, 588, 566, 665, 781,347, 362, 127, 243, 358, 706, 406, 677, 590, 216, 399, 567, 304, 598,359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648, 312,707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571, 410,652, 370, 835, 411, 709, 232, 614, 316, 573, 365, 660, 423, 336, 222,689, 452, 793, 371, 612, 426, 602, 236, 805, 413, 654, 481, 834, 223,713, 344, 603, 318, 544, 454, 655, 427, 615, 373, 776, 434, 560, 238,899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429, 780,239, 676, 360, 837, 400, 626, 246, 663, 678, 435, 568, 458, 817, 350,619, 459, 788, 466, 782, 898, 364, 667, 408, 592, 128, 621, 437, 737,351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366, 790,441, 600, 424, 669, 629, 467, 901, 251, 849, 804, 372, 791, 192, 710,482, 574, 690, 414, 683, 367, 604, 794, 469, 714, 374, 711, 253, 575,656, 483, 807, 415, 685, 905, 375, 616, 224, 633, 806, 428, 795, 865,430, 691, 473, 715, 836, 456, 810, 378, 606, 620, 436, 664, 722, 485,797, 320, 693, 913, 431, 607, 717, 240, 811, 379, 839, 668, 438, 818,622, 460, 838, 723, 248, 697, 381, 738, 680, 462, 813, 628, 489, 900,842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463, 739,684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671, 792,443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416, 825,961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471, 576,716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753, 724,799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440, 820,840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930, 672,917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846, 921,472, 823, 852, 731, 498, 881, 743, 444, 904, 826, 501, 688, 446, 933,847, 636, 963, 733, 937, 476, 854, 827, 447, 746, 868, 638, 908, 800,488, 696, 747, 829, 858, 754, 855, 916, 965, 478, 910, 720, 505, 749,945, 639, 755, 870, 256, 911, 700, 859, 479, 918, 871, 728, 494, 874,969, 932, 702, 816, 861, 500, 757, 492, 875, 732, 923, 824, 977, 919,934, 744, 761, 882, 495, 703, 922, 877, 935, 828, 848, 734, 503, 883,938, 384, 964, 748, 506, 856, 925, 993, 735, 502, 830, 966, 939, 885,946, 750, 860, 756, 480, 967, 831, 889, 941, 751, 872, 507, 971, 912,758, 947, 970, 862, 978, 448, 876, 920, 640, 759, 949, 863, 762, 509,973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926, 879,981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948, 832,508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510, 864,982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511, 766,957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894, 1011,958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000, 1006,990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019,960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S17: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 257, 21, 35, 25, 66, 37, 8, 67, 130, 12, 41, 20, 133, 514,14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261,517, 38, 26, 97, 68, 265, 42, 145, 29, 161, 70, 50, 75, 43, 521, 273,193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 134, 321, 53, 77,83, 138, 57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44,99, 141, 31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577,76, 267, 105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525,84, 58, 113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 531, 100, 140,197, 87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91,201, 546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 164, 268,386, 325, 305, 537, 769, 533, 209, 154, 151, 107, 56, 166, 387, 578,329, 549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196,157, 88, 547, 62, 278, 292, 520, 279, 117, 198, 178, 642, 171, 282, 92,553, 202, 199, 389, 294, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 211, 185, 534, 401,306, 301, 643, 156, 110, 327, 539, 116, 168, 593, 158, 111, 307, 548,330, 213, 771, 226, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,180, 777, 200, 229, 554, 339, 657, 313, 541, 391, 123, 582, 394, 284,773, 233, 673, 555, 785, 175, 341, 705, 449, 562, 354, 801, 395, 204,182, 528, 583, 557, 296, 286, 64, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 214, 594, 357, 308, 419, 187, 589, 569, 302, 647, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 160, 218, 610, 597, 552, 651, 230, 120, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 176, 653, 392, 231, 314, 340, 543, 335,234, 556, 775, 124, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,350, 619, 128, 788, 246, 782, 898, 437, 667, 466, 592, 408, 621, 364,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 372, 710,192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374, 575,656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795, 865,224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722, 320,797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240, 818,622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248, 900,842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463, 739,684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671, 443,845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416, 825, 741,254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471, 576, 716, 376,867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753, 724, 799, 490,857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440, 820, 840, 869,493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930, 672, 917, 822,464, 727, 844, 491, 632, 730, 701, 383, 742, 846, 921, 472, 823, 852,731, 498, 881, 743, 444, 904, 688, 826, 501, 933, 847, 446, 636, 746,827, 733, 447, 963, 937, 476, 854, 868, 638, 908, 488, 696, 747, 829,754, 855, 858, 916, 965, 478, 910, 720, 800, 700, 494, 505, 749, 945,859, 639, 755, 256, 969, 479, 384, 870, 492, 911, 816, 918, 728, 871,874, 702, 932, 861, 500, 757, 732, 824, 923, 875, 977, 919, 503, 934,744, 761, 882, 495, 703, 922, 848, 993, 448, 502, 877, 734, 828, 883,935, 964, 506, 938, 748, 856, 925, 735, 830, 966, 939, 885, 507, 750,946, 860, 756, 480, 967, 831, 889, 941, 751, 872, 971, 912, 758, 947,970, 862, 978, 876, 920, 640, 759, 949, 863, 762, 509, 973, 924, 878,953, 887, 936, 979, 763, 504, 884, 704, 994, 926, 879, 981, 942, 765,496, 927, 886, 995, 736, 940, 985, 968, 890, 948, 832, 508, 943, 752,974, 997, 891, 950, 760, 893, 972, 1001, 954, 510, 864, 982, 951, 975,764, 1009, 980, 880, 955, 987, 996, 892, 928, 511, 766, 957, 998, 983,888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512,1003, 895, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991,1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021,1016, 1008, 1020, 1022, 1023, 1024];

sequence S18: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 12, 130, 41, 69, 14, 20,131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261, 97,145, 27, 514, 39, 515, 265, 68, 42, 29, 161, 70, 43, 517, 50, 71, 273,45, 521, 529, 16, 132, 74, 193, 51, 289, 545, 24, 75, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 85, 30, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 101, 266, 72, 46, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 163, 274, 523, 641, 105, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 195, 290, 79, 169,277, 59, 86, 100, 87, 140, 61, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 106, 322, 293, 201, 323,578, 150, 297, 48, 93, 209, 549, 579, 268, 386, 325, 305, 164, 151, 107,56, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155, 276,60, 271, 115, 167, 524, 581, 561, 157, 196, 170, 198, 171, 278, 292,279, 117, 88, 62, 178, 282, 526, 643, 532, 527, 63, 92, 585, 770, 144,389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534, 645,535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210, 538,95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110, 156,327, 116, 111, 773, 550, 657, 539, 551, 168, 213, 307, 330, 158, 226,118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119,541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 64,394, 284, 175, 123, 341, 449, 354, 395, 233, 204, 673, 555, 557, 562,582, 296, 286, 182, 206, 125, 785, 705, 183, 287, 528, 583, 644, 586,563, 300, 355, 212, 402, 186, 397, 345, 207, 302, 801, 96, 187, 241,536, 587, 565, 646, 594, 328, 403, 214, 357, 308, 303, 833, 589, 647,112, 540, 569, 595, 650, 772, 228, 418, 332, 215, 405, 310, 189, 552,610, 897, 160, 218, 361, 419, 409, 369, 230, 450, 421, 542, 597, 651,774, 658, 311, 120, 334, 219, 543, 611, 231, 392, 234, 314, 176, 340,335, 221, 451, 425, 315, 556, 601, 653, 124, 775, 659, 613, 235, 288,453, 126, 342, 396, 778, 584, 558, 674, 356, 343, 564, 661, 559, 617,779, 675, 184, 398, 433, 317, 346, 242, 208, 404, 358, 786, 188, 588,566, 665, 625, 781, 237, 127, 243, 347, 399, 706, 216, 677, 787, 590,567, 648, 406, 359, 304, 570, 596, 362, 707, 190, 457, 349, 465, 802,420, 407, 245, 410, 591, 681, 789, 571, 598, 363, 573, 220, 422, 599,652, 612, 709, 602, 803, 370, 793, 312, 191, 654, 689, 603, 411, 232,249, 365, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 481,236, 223, 344, 318, 544, 373, 615, 427, 776, 128, 454, 238, 560, 834,805, 713, 835, 662, 809, 605, 618, 721, 780, 434, 898, 319, 455, 837,817, 676, 663, 348, 429, 400, 377, 244, 239, 458, 435, 360, 568, 619,666, 737, 899, 841, 782, 626, 350, 246, 459, 592, 678, 621, 667, 788,572, 783, 627, 679, 408, 364, 351, 192, 247, 437, 466, 412, 461, 250,366, 600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 441, 690,794, 604, 575, 467, 424, 372, 251, 482, 414, 469, 367, 374, 656, 901,806, 711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606,483, 473, 224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 485, 430,456, 722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 378, 436, 813,320, 622, 240, 431, 460, 379, 668, 839, 489, 438, 628, 623, 462, 381,439, 352, 497, 680, 725, 819, 842, 670, 738, 630, 468, 248, 442, 463,470, 443, 252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631,792, 845, 902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903, 687,471, 416, 484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866,907, 716, 694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812, 867,432, 380, 698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490, 699,753, 840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493, 464,672, 930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730,383, 499, 444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904,636, 826, 743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501, 488,638, 505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720,916, 870, 478, 700, 749, 639, 816, 965, 945, 755, 859, 911, 492, 479,728, 918, 871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932, 919,757, 922, 875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877, 848,935, 828, 734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856, 885,939, 506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872,751, 889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759,949, 978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504,926, 879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985,508, 890, 948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974, 893,951, 864, 760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983, 928,996, 766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989, 1002,952, 1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988,1013, 1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960,1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S19: [1, 2, 3, 5, 9, 17, 33, 4, 257, 513, 6, 65, 7, 10, 11,129, 18, 13, 19, 34, 21, 35, 25, 66, 37, 258, 8, 130, 67, 12, 41, 69,514, 20, 14, 131, 49, 15, 73, 259, 22, 133, 36, 23, 81, 26, 137, 38, 27,515, 261, 97, 39, 68, 42, 145, 29, 70, 43, 265, 50, 161, 71, 517, 45,193, 132, 273, 74, 51, 134, 82, 75, 16, 289, 521, 24, 53, 135, 77, 57,83, 260, 28, 138, 98, 529, 40, 262, 85, 139, 30, 146, 44, 321, 545, 99,89, 141, 31, 263, 147, 46, 72, 516, 101, 266, 162, 52, 149, 47, 267,769, 76, 105, 163, 385, 54, 153, 78, 518, 194, 274, 165, 55, 84, 269,577, 136, 58, 113, 275, 79, 195, 519, 59, 290, 169, 86, 140, 277, 522,100, 87, 291, 197, 142, 523, 61, 281, 90, 102, 322, 148, 641, 177, 91,293, 143, 201, 530, 264, 32, 150, 386, 525, 103, 106, 93, 323, 48, 531,164, 268, 151, 209, 546, 297, 107, 154, 325, 533, 166, 56, 276, 114,155, 547, 270, 80, 109, 537, 387, 225, 167, 305, 578, 60, 115, 271, 196,549, 329, 170, 157, 278, 770, 88, 171, 389, 520, 117, 292, 198, 62, 642,279, 178, 92, 579, 337, 199, 282, 144, 524, 63, 393, 121, 553, 294, 202,283, 581, 173, 104, 353, 532, 179, 295, 94, 526, 203, 324, 181, 643,298, 108, 401, 561, 152, 210, 285, 527, 95, 326, 205, 585, 299, 156,771, 306, 211, 110, 534, 417, 168, 327, 645, 185, 301, 548, 116, 449,226, 535, 388, 158, 593, 330, 111, 307, 538, 213, 118, 649, 390, 172,338, 550, 227, 331, 539, 217, 272, 773, 159, 280, 609, 119, 309, 174,551, 391, 122, 580, 333, 200, 554, 180, 229, 657, 313, 175, 541, 339,123, 582, 284, 204, 394, 555, 64, 777, 182, 296, 562, 233, 341, 673,395, 583, 125, 286, 557, 206, 402, 705, 183, 300, 644, 212, 785, 186,345, 586, 241, 397, 563, 207, 287, 646, 96, 594, 403, 302, 587, 214,328, 528, 187, 801, 357, 112, 536, 418, 228, 565, 308, 647, 405, 215,589, 303, 189, 569, 332, 595, 218, 361, 772, 419, 230, 540, 310, 650,160, 409, 610, 334, 552, 120, 450, 774, 219, 597, 421, 231, 651, 311,542, 340, 234, 392, 556, 314, 833, 176, 369, 611, 124, 601, 335, 451,653, 221, 543, 315, 775, 184, 425, 342, 558, 235, 584, 396, 613, 356,126, 778, 343, 674, 453, 564, 242, 398, 661, 208, 559, 317, 779, 346,588, 188, 358, 617, 404, 675, 237, 897, 433, 566, 347, 665, 127, 590,399, 457, 706, 243, 786, 288, 677, 406, 567, 190, 596, 359, 781, 362,648, 216, 570, 349, 625, 304, 245, 787, 420, 591, 407, 707, 465, 220,802, 363, 681, 410, 598, 191, 652, 422, 789, 312, 612, 249, 599, 370,803, 411, 709, 336, 654, 232, 573, 365, 793, 481, 222, 423, 602, 316,614, 371, 834, 236, 660, 452, 689, 426, 603, 413, 805, 223, 655, 344,713, 427, 776, 238, 544, 373, 662, 454, 898, 318, 615, 244, 618, 605,434, 835, 348, 560, 455, 676, 239, 780, 400, 663, 319, 721, 377, 809,458, 619, 128, 666, 429, 837, 678, 360, 568, 435, 788, 246, 626, 350,667, 459, 782, 592, 437, 621, 247, 899, 364, 737, 408, 679, 466, 817,351, 627, 250, 783, 461, 708, 841, 412, 682, 467, 669, 366, 790, 192,600, 683, 424, 901, 441, 629, 804, 372, 710, 482, 574, 251, 791, 690,414, 604, 367, 849, 711, 469, 794, 374, 656, 428, 575, 905, 253, 633,483, 806, 714, 473, 795, 415, 685, 616, 375, 865, 691, 224, 807, 430,606, 715, 378, 836, 456, 693, 810, 436, 620, 913, 485, 664, 431, 722,797, 240, 607, 838, 379, 717, 460, 811, 668, 320, 818, 723, 438, 622,929, 489, 680, 381, 839, 697, 248, 813, 628, 462, 961, 738, 439, 900,468, 842, 623, 442, 819, 725, 497, 630, 463, 902, 684, 252, 850, 739,352, 843, 729, 784, 470, 792, 443, 631, 821, 368, 686, 903, 484, 634,845, 471, 712, 692, 445, 741, 825, 474, 687, 851, 635, 254, 796, 716,486, 906, 576, 416, 866, 694, 808, 376, 745, 853, 475, 907, 637, 487,798, 718, 914, 490, 695, 812, 432, 724, 867, 698, 380, 857, 753, 477,909, 719, 799, 255, 608, 915, 814, 440, 726, 840, 699, 491, 869, 624,382, 930, 740, 820, 498, 917, 727, 815, 464, 701, 844, 730, 444, 873,931, 742, 493, 822, 672, 921, 383, 846, 632, 962, 499, 731, 933, 743,823, 446, 852, 746, 904, 472, 826, 688, 881, 501, 636, 847, 963, 733,256, 827, 696, 937, 476, 854, 747, 908, 868, 447, 638, 855, 965, 754,505, 910, 720, 829, 858, 488, 700, 870, 916, 478, 749, 945, 859, 639,911, 492, 969, 755, 800, 918, 479, 702, 871, 874, 728, 494, 861, 816,757, 932, 919, 500, 977, 732, 875, 922, 703, 495, 934, 824, 761, 882,384, 923, 848, 744, 877, 993, 734, 502, 935, 828, 883, 748, 964, 503,938, 925, 735, 856, 939, 750, 506, 885, 966, 830, 756, 946, 860, 448,967, 751, 912, 831, 889, 970, 507, 640, 941, 872, 947, 758, 862, 971,509, 949, 759, 876, 920, 978, 863, 762, 480, 973, 924, 979, 878, 704,936, 953, 884, 496, 994, 763, 926, 879, 981, 886, 940, 765, 504, 995,985, 927, 887, 736, 942, 890, 968, 948, 997, 508, 943, 752, 891, 972,832, 950, 1001, 893, 760, 974, 951, 510, 980, 954, 1009, 975, 764, 864,982, 955, 880, 996, 983, 957, 986, 511, 766, 998, 928, 888, 987, 999,1002, 944, 892, 989, 767, 952, 1003, 894, 1010, 976, 956, 512, 1005,895, 1011, 958, 984, 1013, 768, 988, 959, 1017, 1000, 990, 1004, 991,1006, 1012, 1007, 896, 1014, 1015, 1018, 960, 1019, 1021, 992, 1008,1016, 1020, 1022, 1023, 1024]; and

sequence S20: [1, 2, 3, 5, 9, 17, 33, 4, 6, 513, 65, 7, 10, 11, 129, 18,13, 19, 34, 257, 21, 35, 25, 66, 37, 67, 8, 12, 130, 41, 69, 14, 514,20, 131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261,515, 97, 145, 27, 39, 265, 68, 42, 29, 161, 70, 43, 50, 75, 517, 273,193, 71, 45, 132, 16, 74, 289, 51, 24, 53, 521, 134, 82, 321, 77, 135,28, 57, 83, 138, 260, 529, 40, 98, 385, 30, 85, 139, 262, 146, 545, 31,99, 44, 89, 141, 263, 147, 72, 516, 266, 46, 101, 162, 52, 149, 47, 518,76, 267, 163, 274, 105, 54, 153, 577, 78, 269, 194, 165, 275, 55, 519,84, 136, 58, 113, 195, 290, 522, 79, 169, 277, 59, 86, 61, 523, 87, 140,100, 197, 90, 641, 291, 281, 142, 177, 91, 102, 530, 148, 143, 32, 103,264, 525, 106, 322, 293, 201, 531, 323, 150, 297, 48, 93, 546, 209, 268,386, 325, 769, 305, 164, 151, 107, 533, 56, 154, 225, 387, 329, 547,270, 114, 80, 537, 166, 109, 155, 276, 578, 60, 271, 115, 167, 549, 157,196, 170, 198, 579, 171, 278, 292, 520, 279, 117, 88, 62, 524, 178, 282,63, 642, 92, 144, 389, 294, 553, 199, 104, 337, 581, 173, 283, 202, 526,121, 179, 295, 532, 94, 152, 324, 643, 393, 298, 203, 561, 108, 285,181, 527, 210, 95, 205, 585, 299, 353, 326, 770, 185, 211, 534, 401,306, 301, 645, 110, 156, 327, 548, 116, 111, 593, 168, 213, 307, 535,330, 158, 771, 226, 118, 172, 538, 331, 227, 649, 388, 309, 217, 550,417, 338, 773, 159, 272, 609, 119, 280, 657, 333, 390, 174, 539, 122,200, 551, 180, 229, 777, 339, 313, 580, 391, 123, 554, 394, 284, 541,64, 175, 341, 673, 449, 354, 582, 395, 233, 555, 204, 296, 562, 286,587, 182, 206, 785, 125, 183, 705, 287, 300, 583, 355, 212, 557, 402,186, 644, 397, 345, 528, 207, 302, 586, 96, 801, 187, 241, 563, 328,403, 536, 214, 565, 357, 308, 646, 303, 112, 594, 228, 833, 418, 332,589, 215, 405, 647, 310, 540, 189, 160, 569, 218, 361, 595, 419, 650,409, 369, 772, 230, 552, 450, 421, 610, 311, 897, 120, 334, 542, 219,597, 176, 651, 392, 231, 774, 314, 658, 124, 340, 543, 335, 611, 221,451, 556, 425, 601, 315, 653, 234, 235, 775, 288, 659, 453, 584, 126,778, 342, 396, 558, 356, 613, 343, 674, 184, 398, 564, 433, 661, 317,559, 346, 588, 242, 208, 779, 404, 675, 358, 786, 188, 617, 237, 566,127, 665, 243, 347, 590, 399, 781, 216, 706, 406, 677, 359, 787, 304,567, 362, 596, 190, 648, 457, 570, 349, 465, 625, 420, 707, 407, 802,245, 591, 410, 681, 363, 789, 220, 571, 422, 598, 370, 573, 312, 599,191, 652, 411, 612, 232, 709, 249, 602, 365, 803, 336, 793, 423, 316,222, 654, 371, 689, 426, 603, 452, 614, 413, 660, 481, 655, 236, 544,223, 615, 344, 776, 318, 618, 373, 834, 427, 805, 128, 713, 454, 835,238, 662, 809, 434, 560, 319, 605, 455, 721, 348, 780, 429, 898, 400,837, 377, 817, 244, 676, 239, 663, 458, 619, 568, 435, 666, 360, 737,350, 899, 246, 841, 459, 782, 626, 408, 592, 364, 678, 351, 621, 437,667, 192, 788, 572, 247, 783, 466, 627, 412, 679, 669, 461, 708, 250,682, 366, 710, 441, 683, 790, 467, 804, 424, 791, 629, 372, 600, 251,574, 414, 690, 794, 367, 575, 469, 604, 656, 482, 901, 374, 806, 428,711, 616, 415, 849, 253, 685, 795, 483, 714, 473, 633, 691, 224, 807,606, 375, 664, 485, 836, 905, 430, 810, 456, 715, 620, 378, 797, 693,436, 722, 320, 607, 717, 240, 811, 865, 431, 838, 460, 697, 723, 379,913, 818, 489, 813, 622, 438, 668, 462, 839, 628, 381, 623, 680, 439,725, 819, 352, 842, 670, 497, 738, 630, 468, 684, 843, 248, 739, 442,900, 821, 463, 729, 929, 470, 850, 671, 784, 443, 631, 792, 252, 845,902, 368, 686, 634, 254, 712, 692, 471, 741, 851, 416, 825, 903, 484,635, 906, 796, 445, 576, 687, 376, 853, 961, 474, 866, 907, 745, 486,716, 808, 475, 798, 694, 255, 718, 637, 695, 432, 799, 812, 380, 867,724, 914, 487, 698, 909, 477, 857, 719, 814, 490, 608, 699, 753, 440,840, 915, 726, 491, 869, 820, 382, 815, 624, 740, 498, 930, 844, 727,493, 917, 822, 701, 464, 672, 730, 873, 383, 931, 921, 881, 499, 742,962, 933, 444, 823, 632, 846, 731, 446, 688, 904, 743, 472, 826, 636,852, 447, 847, 733, 963, 937, 256, 827, 746, 747, 476, 800, 965, 638,854, 501, 908, 868, 855, 696, 488, 910, 945, 829, 858, 505, 754, 720,916, 478, 870, 700, 749, 639, 755, 492, 859, 911, 728, 918, 479, 871,816, 874, 702, 384, 969, 861, 977, 932, 919, 494, 757, 922, 875, 732,934, 500, 882, 824, 703, 923, 495, 744, 761, 877, 848, 935, 828, 502,734, 883, 938, 964, 925, 448, 993, 748, 735, 856, 830, 885, 503, 939,640, 966, 750, 946, 831, 506, 967, 860, 941, 912, 889, 756, 507, 751,970, 947, 872, 862, 758, 971, 480, 920, 876, 863, 949, 704, 759, 978,509, 924, 973, 762, 878, 953, 979, 936, 884, 496, 763, 926, 879, 981,994, 886, 940, 927, 504, 765, 995, 985, 736, 887, 997, 942, 968, 890,948, 508, 832, 752, 943, 972, 891, 1001, 950, 974, 893, 951, 864, 510,1009, 980, 760, 975, 982, 764, 880, 766, 983, 928, 996, 511, 957, 888,986, 998, 987, 767, 944, 892, 999, 989, 1002, 952, 1003, 894, 1010,1005, 976, 512, 895, 1011, 956, 958, 984, 959, 768, 988, 1013, 1000,1017, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 960, 1015, 1018,1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024].

The foregoing sequences with relatively good performance that areobtained through simulation may be compared by using a presetperformance determining rule. Optionally, this embodiment of thisapplication provides an example of a performance determining rule, butthis is not limited thereto.

A possible performance determining rule is described as follows.

Evaluation measurement: signal-to-noise ratios (SNR) required when ablock error rate (BLER) reaches 10⁼² and 10⁼³.

Simulation assumption:

Channel Additive white Gaussian noise (AWGN) channel Modulation modeQuadrature phase shift keying (QPSK) Information code K = [8, min (200,K_(max,N)], where block length K (K K_(max,N) = └5N/6 − (J + J′)┘ doesnot include K = min(200, K), K_(max,N)], K_(max,N)], where a CRC bit)K_(max,N) = └5N/6 − (J + J′)┘ A K value that enables a bit rate to beless than ⅛ is not considered. Code length N {64, 128, 256, 512, 1024}Decoding algorithm LLR-based min-sum decoding algorithm for a list-XSize of a list X 1, 2, 4, 8, and 16 (CRC check is performed by usingonly eight best paths) Construction method CA polar Quantity of (J + J′)19 bits (0b10100010101101111001, where a last bit is d19)

SNR values required when a BLER reaches 10⁼² and 10⁼³ are respectivelyevaluated. To be specific, sequences A and B are given. Each combination(N,K) is investigated based on the simulation parameter in the foregoingtable. For example, N=64, and K=10. An SNR value required when BLER=10⁻²by a polar code using the sequence A is denoted as HA, and an SNR valuerequired when BLER=10⁻² by a polar code using the sequence B is denotedas HB. An interpolation HA-HB of the SNR values is compared with a giventhreshold. If the interpolation HA-FIB is greater than the threshold, itis recorded that the sequence B wins, a win count of the sequence B isincremented by 1, and a fail count of the sequence A is incrementedby 1. If the interpolation HA-HB is less than a negative threshold, itis recorded that the sequence A wins, a win count of the sequence A isincremented by 1, and a fail count of the sequence B is incrementedby 1. If the interpolation HA-HB is less than or equal to the thresholdor greater than or equal to the negative threshold, it is recorded thatthe two sequences have same performance, and neither of the win countsof the two sequences is incremented. Further, SNR values required by thesequences A and B when BLER=10⁻³ is reached are further investigated, aninterpolation is compared with a threshold, and an operation is furtherperformed on a win count.

Steps of determining the foregoing threshold are as follows.

When a length K of to-be-coded information is less than or equal to 200,PerfThresh_K=0.1 dB; or when K is greater than 200, PerfThresh_K=0.3 dB.

When a quantity of decoding lists is L=1, PerfThresh_L=0.4 dB; when L=2,PerfThresh_L=0.2 dB; or when L is another value, PerfThresh_L=0.1 dB.

A larger value in the two thresholds is selected as a final threshold,that is, PerfThresh=max (PerfThresh_K, PerfThresh_L).

A specific sequence comparison procedure is as follows.

Step 1: Calculate a win count, a fail count, and an overall fail countfor each sequence. The sequence A is selected, and the sequence A iscompared with the sequence B in each simulation case. For eachsimulation case, if performance of A is worse than that of B byPerfThresh, a fail count FailCount_AB of A versus B is incremented by 1;or if performance of A is better than that of B by PerfThresh, a wincount WinCountAB of A versus B is incremented by 1. If (FailCount_AB−WinCountAB)/a total quantity of simulation cases >2%, an overall failcount OverallFail_A of A is incremented by 1. The sequence A is comparedwith a sequence C in each simulation case. For each simulation case, ifthe performance of A is worse than that of C by PerfThresh, a fail countFailCount_AC of A versus C is incremented by 1; or if the performance ofA is better than that of C by PerfThresh, a quantity of win timesWinCount_AC of A versus C is incremented by 1. If(FailCount_AC−WinCount_AC)/a total quantity of simulation cases >2%, theoverall fail count OverallFail_A of A is incremented by 1. The processis repeated for sequences D to N. The sequence B is selected, and thesequence B is compared with the sequence B in each simulation case, andso on. The sequence N is selected, and the sequence N is compared withthe sequence A, and so on. A sequence with a minimum overall fail countOverallFail is selected.

Step 2: If a plurality of sequences A to M each have a minimum overallfail count OverallFail, for the sequence A, the sequence A is comparedwith the sequence B in each simulation case. For each simulation case,if the performance of A is better than that of B by PerfThresh, the wincount WinCount_AB of A versus B is incremented by 1. The sequence A iscompared with the sequence C in each simulation case. For eachsimulation case, if the performance of A is better than that of C, byPerfThresh, the win count WinCount_AC of A versus C is incremented by 1,and an overall win count of A is WinCount A=ΣWinCount_AB . . . AM. Theprocess is repeated until the sequence A is compared with the sequenceM. The process is repeated for sequences B to M. A sequence with amaximum overall win count WinCount is selected, and it is assumed thatthe sequence is a sequence W.

Step 3: The sequence W with a maximum overall win count is given. Ifthere is a sequence x and a win count of x for W is greater than a wincount of W for x, namely WinCount_xW>WinCount Wx, the sequence x is alsoselected to enter a next round.

Step 4: If a plurality of sequences are selected, a final sequence isdetermined through voting.

It should be noted that the foregoing sequences S1 to S20 may be appliedin the polar coding method shown in FIG. 2 in this embodiment of thisapplication. In any sequence, adjustments or equivalent replacementsincluding but not limited to the following several aspects may be madewithout affecting an overall effect of the sequence.

1. Locations of a few elements in a sorting sequence are mutuallyexchanged. For example, a location of a sequence number may be adjustedwithin a specified amplitude. For example, the specified amplitude is 5,and a location of an element whose sequence number is 10 may be adjustedwithin a range from five locations on the left of the element to fivelocations on the right of the element.

2. Some elements in the sorting sequence are adjusted, but sets ofchannels that are used to transmit T-bit information and that areselected based on the sorting sequence may be the same or similar.

3. The sorting sequence includes N elements from 1 to N, and the Nelements from 1 to N represent sequence numbers of N polarized channels.Actually, the sequence numbers of the N polarized channels may beginwith 0 and end with N−1, and the sequence numbers may be obtained bysubtracting 1 from each sequence number in the sorting sequence. This isalso a form of a sequence number in the foregoing calculation manner.Certainly, another manner may alternatively be used to represent thesequence numbers or identifiers of the polarized channels, and thespecific expression manner does not affect specific locations of thepolarized channels represented in the sorting sequence.

4. The sequence numbers of the N polarized channels in the sortingsequence are arranged in descending order of reliability of the Npolarized channels. Actually, the sequence numbers of the N polarizedchannels may alternatively be arranged in ascending order of reliabilityof the N polarized channels. Elements in the sorting sequence arearranged in a reverse order.

5. The sorting sequence may further be represented by using a sortingsequence of normalized reliability or equivalent reliability of all thechannels. For example, if a sorting location of a channel x in thesequence is y (a minimum sequence number in the sorting sequence isdenoted as 1), reliability of the channel may be represented by y ornormalized y/N, where N is a length of the sorting sequence.

Based on the polar coding method shown in FIG. 2, as shown in FIG. 3, anembodiment of this application further provides a polar coding apparatus300. The polar coding apparatus 300 is configured to perform the polarcoding method shown in FIG. 2. The Polar coding apparatus 300 includes:

a determining unit 301, configured to determine a sequence used to codeto-be-coded bits, where the sequence is used to represent a reliabilityorder of N polarized channels, N is a mother code length of a polarcode, and N is a positive integer power of 2; and

a coding unit 302, configured to perform polar coding on the to-be-codedbits by using the sequence to obtain coded bits.

Optionally, a length of the to-be-coded bits is K, the K to-be-codedbits are mapped to K polarized channels in the N polarized channels, andreliability of the K polarized channels is higher than reliability ofremaining N−K polarized channels.

Optionally, the sequence may be a part or all of any one of thesequences (1) to (30) in the foregoing method, or may be a part or allof any one of the sequences S1 to S20 in the foregoing method.

Based on a same inventive concept as the polar coding method shown inFIG. 2, as shown in FIG. 4, an embodiment of this application furtherprovides a polar coding apparatus 400. The polar coding apparatus 400 isconfigured to perform the polar coding method shown in FIG. 2. A part orall of the polar coding method shown in FIG. 2 may be implemented byhardware or may be implemented by software. When the method isimplemented by using hardware, the polar coding apparatus 400 includes:an input interface circuit 401, configured to obtain to-be-coded bits; alogic circuit 402, configured to perform the polar coding method shownin FIG. 2, where reference may be made to the description in theforegoing method embodiment and details are not described herein again;and an output interface circuit 403, configured to output a coded bitsequence.

Optionally, in a specific implementation, the polar coding apparatus 400may be a chip or an integrated circuit.

Optionally, when a part or all of the polar coding method in theforegoing embodiment are implemented by using software, as shown in FIG.5, the polar coding apparatus 400 includes: a memory 501, configured tostore a program; and a processor 502, configured to execute the programstored in the memory 501. When the program is executed, the polar codingapparatus 400 may implement the polar coding method provided in theforegoing embodiment in FIG. 2.

Optionally, the memory 501 may be a physically independent unit, or asshown in FIG. 6, the memory 501 is integrated into the processor 502.

Optionally, when a part or all of the coding method in the foregoingembodiment in FIG. 2 are implemented by using software, the polar codetransmission apparatus 400 may include only the processor 502. Thememory 501 configured to store a program is located outside the polarcode transmission apparatus 400. The processor 502 is connected to thememory 501 by using a circuit/wire, and is configured to read andexecute the program stored in the memory 501.

The processor 502 may be a central processing unit (CPU), a networkprocessor (NP), or a combination of a CPU and an NP.

The processor 502 may further include a hardware chip. The hardware chipmay be an application-specific integrated circuit (ASIC), a programmablelogic device (PLD), or a combination thereof. The PLD may be a complexprogrammable logical device (CPLD), a field-programmable gate array(FPGA), generic array logic (GAL), or any combination thereof.

The memory 501 may include a volatile memory, such as a random accessmemory (RAM); the memory 501 may include a nonvolatile memory, such as aflash memory, a hard disk drive (HDD), or a solid-state drive (SSD); orthe memory 501 may include a combination of the foregoing types ofmemories.

An embodiment of this application further provides a computer storagemedium. The computer storage medium stores a computer program, and thecomputer program includes an instruction used to perform the polarcoding method shown in FIG. 2.

An embodiment of this application further provides a computer programproduct including an instruction. When the computer program product runson a computer, the computer performs the polar coding method shown inFIG. 2.

A person skilled in the art should understand that the embodiments ofthis application may be provided as a method, a system, or a computerprogram product. Therefore, this application may use a form ofhardware-only embodiments, software-only embodiments, or embodimentswith a combination of software and hardware. Moreover, this applicationmay use a form of a computer program product that is implemented on oneor more computer-usable storage media (including but not limited to adisk memory, a CD-ROM, an optical memory, and the like) that includecomputer usable program code.

This application is described with reference to the flowcharts and/orblock diagrams of the method, the device (system), and the computerprogram product according to the embodiments of this application. Itshould be understood that computer program instructions may be used toimplement each process and/or each block in the flowcharts and/or theblock diagrams and a combination of a process and/or a block in theflowcharts and/or the block diagrams. These computer programinstructions may be provided for a general-purpose computer, a dedicatedcomputer, an embedded processor, or a processor of any otherprogrammable data processing device to generate a machine, so that theinstructions executed by a computer or a processor of any otherprogrammable data processing device generate an apparatus forimplementing a specific function in one or more processes in theflowcharts and/or in one or more blocks in the block diagrams.

These computer program instructions may be stored in a computer readablememory that can instruct the computer or any other programmable dataprocessing device to work in a specific manner, so that the instructionsstored in the computer readable memory generate an artifact thatincludes an instruction apparatus. The instruction apparatus implementsa specific function in one or more processes in the flowcharts and/or inone or more blocks in the block diagrams.

These computer program instructions may be loaded onto a computer oranother programmable data processing device, so that a series ofoperations and steps are performed on the computer or the anotherprogrammable device, thereby generating computer-implemented processing.Therefore, the instructions executed on the computer or the anotherprogrammable device provide steps for implementing a specific functionin one or more processes in the flowcharts and/or in one or more blocksin the block diagrams.

Although some embodiments of this application have been described, aperson skilled in the art can make changes and modifications to theseembodiments once they learn the basic inventive concept. Therefore, thefollowing claims are intended to be construed as to cover the preferredembodiments and all changes and modifications falling within the scopeof this application.

Obviously, a person skilled in the art can make various modificationsand variations to the embodiments of this application without departingfrom the spirit and scope of the embodiments of the present invention.This application is intended to cover these modifications and variationsprovided that they fall within the scope of protection defined by thefollowing claims and their equivalent technologies.

1. A polar decoding method, comprising: obtaining to-be-decoded bits;determining a sequence with a length N based on a preset sequence,wherein the sequence with the length N is used to represent areliability order of N polarized channels, wherein N is a positiveinteger power of 2, wherein the preset sequence is [1, 2, L₁ ^((m=3))17, L₂ ^((m=1012)), L₃ ^((m=2)), 1020, 1022, 1023, 1024], wherein L_(n)^((m)) is a subsequence in the preset sequence, wherein n is a sequencenumber of the subsequence in preset sequence, wherein n∈{1, 2, 3},wherein m indicates a length of an n^(th) subsequence, and whereinlocations of elements in the subsequence are able to mutually exchangedin the subsequence; and performing polar decoding on the to-be-decodedbits by using the sequence with the length N to obtain decoded bits. 2.The method according to claim 1, wherein the preset sequence comprisessequence numbers of N_(max) polarized channels, wherein the sequencenumbers of the N_(max) polarized channels are arranged in the presetsequence based on reliability of the N_(max) polarized channels, whereinN_(max) is a positive integer power of 2, wherein N_(max)≥N, and whereinN_(max)=1024.
 3. The method according to claim 1, wherein a length ofthe to-be-decoded bits is K, and wherein the K to-be-decoded bits aremapped to K polarized channels in the N polarized channels.
 4. Themethod according to claim 1, wherein L_(n) ^((m)) meets at least one ofthe following conditions: L₁ ^((m=3))=(5, 9, 3); L₂ ^((m=1012))=(33, 7,65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66, 8, 37,67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36,81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145, 29, 70,50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74,515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40, 385, 139,85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519, 266, 162,46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54, 516, 163,269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518, 195, 79,291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90, 281, 102,148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106, 530, 323,150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533, 164, 154,151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225, 167, 276,109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292, 520, 279,117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199, 524, 63, 144,337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94, 324, 561,393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770, 299, 353,326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327, 539, 116,168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172, 551, 331,227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550, 119, 280,538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339, 657, 313,541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64, 341, 705,449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286, 182, 125,206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397, 345, 587,833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357, 589, 569,308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650, 772, 418,540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552, 651, 120,230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369, 231, 653,392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659, 613, 342,778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242, 558, 661,617, 317, 343, 346, 779, 564, 404, 288, 398, 453, 675, 559, 786, 433,188, 358, 208, 665, 588, 781, 706, 677, 237, 347, 566, 362, 127, 243,590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457, 787, 349,245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803, 407, 681,422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709, 481, 614,232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612, 452, 602,426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544, 373, 655,223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244, 721, 455,666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459, 626, 400,663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782, 898, 408,667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682, 250, 627,461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629, 424, 901,467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683, 414, 604,794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685, 905, 253,616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836, 473, 810,378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431, 607, 717,489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438, 697, 462,738, 680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352, 725, 784,470, 630, 819, 439, 670, 463, 739, 684, 252, 843, 850, 497, 902, 821,729, 468, 634, 903, 368, 671, 792, 443, 845, 631, 475, 686, 851, 484,692, 712, 380, 866, 796, 416, 825, 961, 741, 254, 906, 635, 445, 694,745, 486, 808, 687, 907, 471, 576, 716, 376, 867, 914, 474, 853, 637,798, 432, 695, 812, 487, 753, 724, 799, 490, 857, 909, 255, 718, 608,931, 477, 698, 726, 915, 440, 820, 840, 869, 493, 719, 699, 382, 814,624, 815, 499, 873, 740, 930, 672, 917, 822, 464, 727, 962, 844, 491,632, 730, 701, 383, 742, 846, 921, 472, 823, 852, 731, 498, 881, 743,444, 904, 688, 826, 501, 446, 933, 847, 636, 746, 827, 733, 447, 963,937, 476, 854, 868, 638, 908, 488, 696, 747, 829, 754, 855, 858, 916,965, 478, 910, 720, 800, 700, 494, 505, 749, 945, 859, 874, 639, 755,256, 969, 870, 492, 479, 384, 911, 816, 918, 728, 871, 702, 932, 861,500, 757, 732, 824, 923, 875, 977, 919, 503, 934, 744, 761, 882, 495,703, 922, 877, 502, 848, 993, 448, 734, 828, 883, 935, 964, 506, 938,748, 856, 925, 735, 830, 966, 939, 885, 507, 750, 946, 860, 756, 480,967, 831, 889, 941, 751, 872, 971, 912, 758, 947, 970, 862, 978, 876,920, 640, 759, 949, 863, 762, 509, 973, 924, 878, 953, 887, 936, 979,763, 504, 884, 704, 994, 926, 879, 981, 942, 765, 496, 927, 886, 995,736, 940, 985, 968, 890, 948, 832, 508, 943, 752, 974, 997, 891, 950,760, 893, 972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009, 980, 880,955, 987, 996, 892, 928, 511, 766, 957, 998, 983, 888, 986, 944, 999,1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512, 1003, 895, 984,1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012, 768, 1004,1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021); and L₃^((m=2))=(1016, 1008).
 5. A polar decoding apparatus, comprising: atleast one processor; and one or more memories coupled to the at leastone processor and storing programming instructions for execution by theat least one processor to: obtain to-be-decoded bits; determine asequence with a length N based on a preset sequence, wherein thesequence with the length N is used to represent a reliability order of Npolarized channels, wherein N is a positive integer power of 2, whereinthe preset sequence is [1, 2, L₁ ^((m=3)), 17, L₂ ^((m=1012)), L₃^((m=2)), 1020, 1022, 1023, 1024], wherein L_(n) ^((m)) is a subsequencein the preset sequence, wherein n is a sequence number of thesubsequence in the preset sequence, wherein n∈{1, 2, 3}, wherein mindicates a length of an n^(th) subsequence, and wherein locations ofelements in the subsequence are able to be mutually exchanged in thesubsequence; and perform polar decoding on the to-be-decoded bits byusing the sequence with the length N to obtain decoded bits.
 6. Theapparatus according to claim 5, wherein the preset sequence comprisessequence numbers of N_(max) polarized channels, wherein the sequencenumbers of the N_(max) polarized channels are arranged in the presetsequence based on reliability of the N_(max) polarized channels, whereinN_(max) is a positive integer power of 2, and wherein N_(max)≥N andN_(max)=1024.
 7. The apparatus according to claim 5, wherein a length ofthe to-be-decoded bits is K, and wherein the K to-be-decoded bits aremapped to K polarized channels in the N polarized channels.
 8. Theapparatus according to claim 5, wherein L_(n) ^((m)) meets at least oneof the following conditions: L₁ ^((m=3))=(5, 9, 3); L₂ ^((m=1012))=(33,7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66, 8,37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131, 27,36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145, 29,70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135,74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40, 385,139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519, 266,162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54, 516,163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518, 195,79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90, 281,102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106, 530,323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533, 164,154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225, 167,276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292, 520,279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199, 524, 63,144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94, 324,561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770, 299,353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327, 539,116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172, 551,331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550, 119,280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339, 657,313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64, 341,705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286, 182,125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397, 345,587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357, 589,569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650, 772,418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552, 651,120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369, 231,653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659, 613,342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242, 558,661, 617, 317, 343, 346, 779, 564, 404, 288, 398, 453, 675, 559, 786,433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 347, 566, 362, 127,243, 590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457, 787,349, 245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803, 407,681, 422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709, 481,614, 232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612, 452,602, 426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544, 373,655, 223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244, 721,455, 666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459, 626,400, 663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782, 898,408, 667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682, 250,627, 461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629, 424,901, 467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683, 414,604, 794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685, 905,253, 616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836, 473,810, 378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431, 607,717, 489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438, 697,462, 738, 680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352, 725,784, 470, 630, 819, 439, 670, 463, 739, 684, 252, 843, 850, 497, 902,821, 729, 468, 634, 903, 368, 671, 792, 443, 845, 631, 475, 686, 851,484, 692, 712, 380, 866, 796, 416, 825, 961, 741, 254, 906, 635, 445,694, 745, 486, 808, 687, 907, 471, 576, 716, 376, 867, 914, 474, 853,637, 798, 432, 695, 812, 487, 753, 724, 799, 490, 857, 909, 255, 718,608, 931, 477, 698, 726, 915, 440, 820, 840, 869, 493, 719, 699, 382,814, 624, 815, 499, 873, 740, 930, 672, 917, 822, 464, 727, 962, 844,491, 632, 730, 701, 383, 742, 846, 921, 472, 823, 852, 731, 498, 881,743, 444, 904, 688, 826, 501, 446, 933, 847, 636, 746, 827, 733, 447,963, 937, 476, 854, 868, 638, 908, 488, 696, 747, 829, 754, 855, 858,916, 965, 478, 910, 720, 800, 700, 494, 505, 749, 945, 859, 874, 639,755, 256, 969, 870, 492, 479, 384, 911, 816, 918, 728, 871, 702, 932,861, 500, 757, 732, 824, 923, 875, 977, 919, 503, 934, 744, 761, 882,495, 703, 922, 877, 502, 848, 993, 448, 734, 828, 883, 935, 964, 506,938, 748, 856, 925, 735, 830, 966, 939, 885, 507, 750, 946, 860, 756,480, 967, 831, 889, 941, 751, 872, 971, 912, 758, 947, 970, 862, 978,876, 920, 640, 759, 949, 863, 762, 509, 973, 924, 878, 953, 887, 936,979, 763, 504, 884, 704, 994, 926, 879, 981, 942, 765, 496, 927, 886,995, 736, 940, 985, 968, 890, 948, 832, 508, 943, 752, 974, 997, 891,950, 760, 893, 972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009, 980,880, 955, 987, 996, 892, 928, 511, 766, 957, 998, 983, 888, 986, 944,999, 1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512, 1003, 895,984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012, 768,1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021); and L₃^((m=2))=(1016, 1008).
 9. The apparatus according to claim 5, whereinthe polar decoding apparatus is a chip or an integrated circuit.
 10. Apolar decoding apparatus, comprising: an input interface circuit, theinput interface circuit configured to obtain to-be-decoded bits; a logiccircuit, the logic circuit configured to perform: determining a sequencewith a length N based on a preset sequence based on a preset sequence,wherein the sequence with the length N is used to represent areliability order of N polarized channels, wherein N is a positiveinteger power of 2, wherein the preset sequence is [1, 2, L₁ ^((m=3)),17, L₂ ^((m=1012)), L₃ ^((m=2)), 1020, 1022, 1023, 1024], wherein L_(n)^((m)) is a subsequence in the preset sequence, wherein n is a sequencenumber of the subsequence in the preset sequence, wherein n∈{1, 2, 3},wherein m indicates a length of an n^(th) subsequence, and whereinlocations of elements in the subsequence are able to be mutuallyexchanged in the subsequence; and performing polar decoding on theto-be-decoded bits by using the sequence with the length N to obtaindecoded bits; and an output interface circuit, the output interfacecircuit configured to output the decoded bits.
 11. The apparatusaccording to claim 10, wherein the preset sequence comprises sequencenumbers of N_(max) polarized channels, wherein the sequence numbers ofthe N_(max) polarized channels are arranged in the preset sequence basedon reliability of the N_(max) polarized channels, wherein N_(max) is apositive integer power of 2, and wherein N_(max)≥N and N_(max)=1024. 12.The apparatus according to claim 10, wherein a length of theto-be-decoded bits is K, and wherein the K to-be-decoded bits are mappedto K polarized channels in the N polarized channels.
 13. The apparatusaccording to claim 10, wherein L_(n) ^((m)) meets at least one of thefollowing conditions: L₁ ^((m=3))=(5, 9, 3) L₂ ^((m=1012))=(33, 7, 65,513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66, 8, 37, 67,130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81,259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50,75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 515,24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40, 385, 139, 85,30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519, 266, 162, 46,101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54, 516, 163, 269,78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518, 195, 79, 291, 59,277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90, 281, 102, 148, 293,522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106, 530, 323, 150, 297,48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533, 164, 154, 151, 107,56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225, 167, 276, 109, 579,271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292, 520, 279, 117, 171,198, 642, 178, 282, 92, 553, 202, 389, 294, 199, 524, 63, 144, 337, 585,173, 283, 121, 645, 104, 179, 295, 532, 203, 94, 324, 561, 393, 298,152, 581, 210, 285, 181, 526, 108, 95, 205, 770, 299, 353, 326, 527,156, 110, 534, 401, 306, 301, 643, 211, 185, 327, 539, 116, 168, 593,158, 226, 307, 548, 330, 111, 771, 213, 118, 172, 551, 331, 227, 649,388, 309, 159, 609, 417, 338, 535, 217, 272, 550, 119, 280, 538, 333,390, 174, 580, 122, 200, 777, 180, 229, 554, 339, 657, 313, 541, 391,175, 582, 394, 284, 773, 123, 673, 555, 785, 64, 341, 705, 449, 562,354, 801, 395, 233, 204, 528, 583, 557, 296, 286, 182, 125, 206, 241,644, 586, 563, 287, 300, 355, 183, 402, 212, 397, 345, 587, 833, 565,96, 186, 207, 328, 646, 536, 403, 594, 187, 357, 589, 569, 308, 647,419, 214, 302, 228, 303, 897, 595, 361, 112, 650, 772, 418, 540, 215,405, 310, 189, 450, 332, 218, 160, 610, 597, 552, 651, 120, 230, 334,409, 542, 774, 611, 658, 311, 421, 601, 219, 369, 231, 653, 392, 176,314, 340, 543, 335, 124, 556, 775, 234, 315, 659, 613, 342, 778, 451,221, 425, 356, 674, 584, 126, 235, 184, 396, 242, 558, 661, 617, 317,343, 346, 779, 564, 404, 288, 398, 453, 675, 559, 786, 433, 188, 358,208, 665, 588, 781, 706, 677, 237, 347, 566, 362, 127, 243, 590, 406,216, 399, 567, 304, 598, 359, 802, 420, 625, 457, 787, 349, 245, 570,190, 591, 220, 648, 312, 707, 363, 596, 465, 803, 407, 681, 422, 789,249, 599, 191, 571, 370, 652, 410, 835, 411, 709, 481, 614, 232, 573,316, 660, 365, 423, 336, 689, 371, 793, 222, 612, 452, 602, 426, 805,413, 654, 454, 834, 318, 713, 236, 603, 344, 544, 373, 655, 223, 615,427, 776, 434, 560, 238, 899, 618, 348, 809, 244, 721, 455, 666, 319,605, 377, 662, 429, 780, 239, 676, 360, 837, 459, 626, 400, 663, 678,435, 568, 458, 817, 246, 619, 350, 788, 128, 782, 898, 408, 667, 437,592, 364, 621, 466, 737, 351, 679, 572, 247, 682, 250, 627, 461, 708,841, 412, 783, 366, 790, 441, 600, 375, 669, 629, 424, 901, 467, 849,804, 251, 791, 372, 710, 192, 574, 690, 482, 683, 414, 604, 794, 367,714, 469, 711, 374, 575, 656, 428, 807, 415, 685, 905, 253, 616, 483,633, 806, 430, 795, 865, 224, 691, 456, 715, 836, 473, 810, 378, 606,620, 436, 664, 722, 320, 797, 485, 693, 913, 431, 607, 717, 489, 811,460, 839, 668, 240, 818, 622, 379, 838, 723, 438, 697, 462, 738, 680,381, 813, 628, 248, 900, 842, 442, 623, 929, 352, 725, 784, 470, 630,819, 439, 670, 463, 739, 684, 252, 843, 850, 497, 902, 821, 729, 468,634, 903, 368, 671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712,380, 866, 796, 416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486,808, 687, 907, 471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432,695, 812, 487, 753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477,698, 726, 915, 440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815,499, 873, 740, 930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730,701, 383, 742, 846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904,688, 826, 501, 446, 933, 847, 636, 746, 827, 733, 447, 963, 937, 476,854, 868, 638, 908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478,910, 720, 800, 700, 494, 505, 749, 945, 859, 874, 639, 755, 256, 969,870, 492, 479, 384, 911, 816, 918, 728, 871, 702, 932, 861, 500, 757,732, 824, 923, 875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922,877, 502, 848, 993, 448, 734, 828, 883, 935, 964, 506, 938, 748, 856,925, 735, 830, 966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831,889, 941, 751, 872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640,759, 949, 863, 762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504,884, 704, 994, 926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940,985, 968, 890, 948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893,972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987,996, 892, 928, 511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767,989, 952, 1005, 894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956,988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007,1018, 896, 1014, 992, 1019, 960, 1021); and L₃ ^((m=2))=(1016, 1008).14. A non-transitory computer storage medium, wherein the non-transitorycomputer storage medium stores a computer program, and wherein thecomputer program comprises programming instructions for execution by atleast one processor to: obtain to-be-decoded bits; determine a sequencewith a length N based on a preset sequence based on a preset sequence,wherein the sequence with the length N represents a reliability order ofN polarized channels, wherein N is a positive integer power of 2,wherein the preset sequence is [1, 2, L₁ ^((m=3)), 17, L₂ ^((m=1012)),L₃ ^((m=2)), 1020, 1022, 1023, 1024], wherein L_(n) ^((m)) is asubsequence in the preset sequence, wherein n is a sequence number ofthe subsequence in the preset sequence, wherein n∈{1, 2, 3}, wherein mindicates a length of an n^(th) subsequence, and wherein locations ofelements in the subsequence are able to be mutually exchanged in thesubsequence; and perform polar decoding on the to-be-decoded bits byusing the sequence with the length N to obtain decoded bits.
 15. Theapparatus according to claim 14, wherein the preset sequence comprisessequence numbers of N_(max) polarized channels, wherein the N_(max)sequence numbers are arranged in the preset sequence based onreliability of the N_(max) polarized channels, wherein N_(max) is apositive integer power of 2, and wherein N_(max)≥N and N_(max)=1024. 16.The apparatus according to claim 14, wherein a length of theto-be-decoded bits is K, and wherein the K to-be-decoded bits are mappedto K polarized channels in the N polarized channels.
 17. The apparatusaccording to claim 14, wherein L_(n) ^((m)) meets at least one of thefollowing conditions: L₁ ^((m=3))=(5, 9, 3); L₂ ^((m=1012)=()33, 7, 65,513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66, 8, 37, 67,130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81,259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50,75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 515,24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40, 385, 139, 85,30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519, 266, 162, 46,101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54, 516, 163, 269,78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518, 195, 79, 291, 59,277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90, 281, 102, 148, 293,522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106, 530, 323, 150, 297,48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533, 164, 154, 151, 107,56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225, 167, 276, 109, 579,271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292, 520, 279, 117, 171,198, 642, 178, 282, 92, 553, 202, 389, 294, 199, 524, 63, 144, 337, 585,173, 283, 121, 645, 104, 179, 295, 532, 203, 94, 324, 561, 393, 298,152, 581, 210, 285, 181, 526, 108, 95, 205, 770, 299, 353, 326, 527,156, 110, 534, 401, 306, 301, 643, 211, 185, 327, 539, 116, 168, 593,158, 226, 307, 548, 330, 111, 771, 213, 118, 172, 551, 331, 227, 649,388, 309, 159, 609, 417, 338, 535, 217, 272, 550, 119, 280, 538, 333,390, 174, 580, 122, 200, 777, 180, 229, 554, 339, 657, 313, 541, 391,175, 582, 394, 284, 773, 123, 673, 555, 785, 64, 341, 705, 449, 562,354, 801, 395, 233, 204, 528, 583, 557, 296, 286, 182, 125, 206, 241,644, 586, 563, 287, 300, 355, 183, 402, 212, 397, 345, 587, 833, 565,96, 186, 207, 328, 646, 536, 403, 594, 187, 357, 589, 569, 308, 647,419, 214, 302, 228, 303, 897, 595, 361, 112, 650, 772, 418, 540, 215,405, 310, 189, 450, 332, 218, 160, 610, 597, 552, 651, 120, 230, 334,409, 542, 774, 611, 658, 311, 421, 601, 219, 369, 231, 653, 392, 176,314, 340, 543, 335, 124, 556, 775, 234, 315, 659, 613, 342, 778, 451,221, 425, 356, 674, 584, 126, 235, 184, 396, 242, 558, 661, 617, 317,343, 346, 779, 564, 404, 288, 398, 453, 675, 559, 786, 433, 188, 358,208, 665, 588, 781, 706, 677, 237, 347, 566, 362, 127, 243, 590, 406,216, 399, 567, 304, 598, 359, 802, 420, 625, 457, 787, 349, 245, 570,190, 591, 220, 648, 312, 707, 363, 596, 465, 803, 407, 681, 422, 789,249, 599, 191, 571, 370, 652, 410, 835, 411, 709, 481, 614, 232, 573,316, 660, 365, 423, 336, 689, 371, 793, 222, 612, 452, 602, 426, 805,413, 654, 454, 834, 318, 713, 236, 603, 344, 544, 373, 655, 223, 615,427, 776, 434, 560, 238, 899, 618, 348, 809, 244, 721, 455, 666, 319,605, 377, 662, 429, 780, 239, 676, 360, 837, 459, 626, 400, 663, 678,435, 568, 458, 817, 246, 619, 350, 788, 128, 782, 898, 408, 667, 437,592, 364, 621, 466, 737, 351, 679, 572, 247, 682, 250, 627, 461, 708,841, 412, 783, 366, 790, 441, 600, 375, 669, 629, 424, 901, 467, 849,804, 251, 791, 372, 710, 192, 574, 690, 482, 683, 414, 604, 794, 367,714, 469, 711, 374, 575, 656, 428, 807, 415, 685, 905, 253, 616, 483,633, 806, 430, 795, 865, 224, 691, 456, 715, 836, 473, 810, 378, 606,620, 436, 664, 722, 320, 797, 485, 693, 913, 431, 607, 717, 489, 811,460, 839, 668, 240, 818, 622, 379, 838, 723, 438, 697, 462, 738, 680,381, 813, 628, 248, 900, 842, 442, 623, 929, 352, 725, 784, 470, 630,819, 439, 670, 463, 739, 684, 252, 843, 850, 497, 902, 821, 729, 468,634, 903, 368, 671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712,380, 866, 796, 416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486,808, 687, 907, 471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432,695, 812, 487, 753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477,698, 726, 915, 440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815,499, 873, 740, 930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730,701, 383, 742, 846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904,688, 826, 501, 446, 933, 847, 636, 746, 827, 733, 447, 963, 937, 476,854, 868, 638, 908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478,910, 720, 800, 700, 494, 505, 749, 945, 859, 874, 639, 755, 256, 969,870, 492, 479, 384, 911, 816, 918, 728, 871, 702, 932, 861, 500, 757,732, 824, 923, 875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922,877, 502, 848, 993, 448, 734, 828, 883, 935, 964, 506, 938, 748, 856,925, 735, 830, 966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831,889, 941, 751, 872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640,759, 949, 863, 762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504,884, 704, 994, 926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940,985, 968, 890, 948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893,972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987,996, 892, 928, 511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767,989, 952, 1005, 894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956,988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007,1018, 896, 1014, 992, 1019, 960, 1021); and L₃ ^((m=2))=(1016, 1008).